12^2=x(x+2+x)

Solution for 12^2=x(x+2+x) equation:

12^2=x(x+2+x)

We move all terms to the left:

12^2-(x(x+2+x))=0

We add all the numbers together, and all the variables

-(x(2x+2))+12^2=0

We add all the numbers together, and all the variables

-(x(2x+2))+144=0


We calculate terms in parentheses: -(x(2x+2)), so:

x(2x+2)

We multiply parentheses

2x^2+2x

Back to the equation:

-(2x^2+2x)


We get rid of parentheses

-2x^2-2x+144=0

a = -2; b = -2; c = +144;
Δ = b2-4ac
Δ = -22-4·(-2)·144
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-34}{2*-2}=\frac{-32}{-4}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+34}{2*-2}=\frac{36}{-4}
=-9
$