x^2+10x=-2x

Solution for x^2+10x=-2x equation:

x^2+10x=-2x

We move all terms to the left:

x^2+10x-(-2x)=0

We get rid of parentheses

x^2+10x+2x=0

We add all the numbers together, and all the variables

x^2+12x=0

a = 1; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·1·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*1}=\frac{0}{2}
=0
$