Linear equations solver calculator
Calculator finds out solution of linear equation given in general ax+b=0 form.

Beta version#

This online calculator is currently under heavy development. It may or it may NOT work correctly.
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Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

Input equation, which you want to solve#

Parameters of the ax + b = 0 equation
Coefficient a
(just before x)
Free parameter b
Unknown variable
(the variable, which we're searching for)

The solution of your equation#

The equation you entered
Show source2 x+5=02~x+5 = 0
The solution of the equation
Show sourcex=52x = \frac{-5}{2}

The solution step-by-step#

I. We subtract free term (b) from both sides.
2 x+55=052~x+\cancel{5}-{\color{#ffff33}{\cancel{5}}} = 0 -{\color{#ffff33}{5}}2 x=52~x = -5
II. We divide both sides by coefficient standing just before x (a).
2x2=52\frac{\cancel{2}\cdot x}{{\color{#ffff33}{\cancel{2}}}} = \frac{-5}{{\color{#ffff33}{2}}}x=52\begin{aligned}x& = \frac{-5}{2}\end{aligned}

Some facts#

  • Linear equation is an equation that can be presented in the form:
    ax+b=0ax + b = 0
    • a, b - fixed parameters, these are numbers which we know,
    • x - unknown variable, this is the number we're searching for.
  • To solve the equation, we need to find a number that, after inserting in the place of x, will make the equation true. Then we say that the number x meets the equation or x is the solution of the equation.
  • When we're solving the linear equation, we're trying to get to the situation where the unknown is on the left side, and the right side contains only known numbers.
  • The equation can be freely transformed by performing the same operations on both sides e.g. dividing both sides by the same number.
  • If we have a linear equation in the form ax+b=0ax + b = 0, we can find a solution by following steps below:
    • 1. We subtract the number b from both sides:
      ax+bb=0bax + b - b = 0 - b
      then we get:
      ax=bax = -b
    • 2. We divide both sides by the number standing at x (a):
      axa=ba\dfrac{ax}{a} = -\dfrac{b}{a}
      then the number a on the left side can be cancelled:
      axa=ba\dfrac{\cancel{a}x}{\cancel{a}} = -\dfrac{b}{a}
    • 3. We get a solution:
      x=bax = -\dfrac{b}{a}
  • Linear equation is also called the first degree equation . The name comes from the fact that in the linear equation an unknown x exists in the first power.
  • You can find more about different types of equations by visiting our other calculator: Equation types.

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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