General equations solver calculator
Calculator finds out solution of equation given in any L=R form.

Beta version#

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Input equation, which you want to solve#

Parameters of the equation
Left side
Right side

The solution of your equation#

The equation you entered
Show source2 x=52~ x = 5
The solution of the equation
Show sourcex=52x = \frac{5}{2}

The solution step-by-step#

1. Divide from both sides:(2 x)2=52\frac{\left(2~ x\right)}{2} = \frac{5}{2}
2. Simplify fraction:x=52 x = \frac{5}{2}

Some facts#

  • In the equation some part is known, and another one is unknown.
  • Solving the equation consists of finding what to substitute in place of the unknown to get the true sentence (equality) . We say then that solution satisfies the equation.
    ⓘ Example: The solution of the equation:
    2+x=52 + x = 5
    is number 3 because when we replace x by it we get:
    2+3=52 + 3 = 5
    so:
    5=55 = 5
  • Equations generally reflect some practical problems in which we seek a value that meets our criteria e.g.:
    • we know that 6 eggs are needed for one cheesecake, we want to know how many eggs we need to bake two cheesecakes for the upcoming holidays,
    • we need to get to a city 300 km away, we wonder how long time it will take us on a trip if we were going on average at 50 km/h,
    • we have pocket money of 10$ per week and we would like to buy a bike for 500$, we wonder how many weeks we have to put off to buy it,
      [Li]etc.
  • Equations can be divided due to the type of object we are looking for (type of solution):
    • number equations - if the solution is the number (e.g. number 3), we are looking for answers to questions like:
      • "how much"
      • "how many",
      • "at what price",
      • "is there a number that...",
      • etc.
      Example number equation is (x is an unknown number):
      x=x+1x = x + 1
    • functional equations - if solution is a function (e.g. f(x) = 3x2 - 5), we are looking for answers to questions such as:
      • "is there a function that ...",
      • "after which the track will move ...",
      • "how one value depends on another one",
      • "the derivative of what function is ...",
      • etc.
      An example of a functional equation is (f is an unknown function):
      ddxf(x)=2x4\dfrac{d}{dx} f(x) = 2x-4
    • etc.
  • Number equations are often divided due to type of expression that they contain, for example:
    • linear equation - x is an unknown, a and b are known parameters:
      ax+b=0ax + b = 0
    • quadratic equation - x is an unknown, a, b and c are known parameters:
      ax2+bx+c=0ax ^ 2 + bx + c = 0
    • polynomial equation - x is an unknown, polynomial coefficients are known:
      W(x)=anxn+an1xn1+an2xn2a1x+a0=0W(x) = a_n x^n + a_{n-1} x^{n-1} + a_{n-2} x^{n-2} \dots a_1 x + a_0 = 0
    • exponential equation - unknown x occurs in the exponent of power:
      axb=0a^x - b = 0
    • logarithmic equation - unknown x occurs under the logarithm:
      log(x)b=0log(x) - b = 0
    • etc.
  • Equations can also be divided due to the amount of unknowns:
    • equations with one unknown, e.g.
      x=x+1x = x + 1
    • equation with two unknowns, e.g.
      x+y=3x + y = 3
    • etc.
  • Equations can have more than one solution (our problem can be solved in different ways) or has no solutions (our problem can't be solved in that way). Depending on the number of solutions, the equation can be divided into:
    • identity equation - there are infinitely many of solutions e.g.
      2(x1)+2=2x2(x - 1) + 2 = 2x
      (we can find any number of different numbers that when can substituted for x and get the true sentence)
    • contradictory equations - there is no solution, e.g.:
      sin(x)=10sin(x) = 10
      (there is no such number whose sine is 10)

See also#

If you are interested in solving mathematical equations, check out our other calculators:
  • Linear equation solver - see how to solve a linear equation in the form ax+b=0ax + b = 0 step by step,
  • Quadratic equation solver - see how to solve quadratic equation in the form ax2+bx+c=0ax ^ 2 + bx + c = 0 using the so-called delta scheme,
  • General equation solver - if you don't know which solving method should be applied to your equation, just give us the left and right side and we will try to solve it for you.

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