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

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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 source $2~x+5 = 0$
The solution of the equation
Show source $x = \frac{-5}{2}$

The solution step-by-step#

I. We subtract free term (b) from both sides.

2~x+\cancel{5}-{\color{#ffff33}{\cancel{5}}} = 0 -{\color{#ffff33}{5}}

2~x = -5

II. We divide both sides by coefficient standing just before x (a).

\frac{\cancel{2}\cdot x}{{\color{#ffff33}{\cancel{2}}}} = \frac{-5}{{\color{#ffff33}{2}}}

\begin{aligned}x& = \frac{-5}{2}\end{aligned}

Some facts#

Linear equation is an equation that can be presented in the form:

$ax + b = 0$
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 $ax + b = 0$ , we can find a solution by following steps below:
- 1. We subtract the number b from both sides:
  
  $ax + b - b = 0 - b$
  then we get:
  
  $ax = -b$
- 2. We divide both sides by the number standing at x (a):
  
  $\dfrac{ax}{a} = -\dfrac{b}{a}$
  then the number a on the left side can be cancelled:
  
  $\dfrac{\cancel{a}x}{\cancel{a}} = -\dfrac{b}{a}$
- 3. We get a solution:
  
  $x = -\dfrac{b}{a}$
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.