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

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Input equation, which you want to solve

Parameters of the ax + b = 0 equation
Coefficient a
(just before x)
Free parameter b

The solution of your equation

The equation you entered
Show source2x+5=02\cdot 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.
2x+55=052\cdot x+\cancel{5}-{\color{#ffff33}{\cancel{5}}} = 0 -{\color{#ffff33}{5}}2x=52\cdot 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=52\begin{aligned}x& = \frac{-5}{2} = \frac{-5}{2}\end{aligned}

Some facts

  • Linear equation is an equation that can be presented in the form:
    ax+b=0ax + b = 0
    where:
    • 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.

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