8^2=x(12+x)

Solution for 8^2=x(12+x) equation:

8^2=x(12+x)

We move all terms to the left:

8^2-(x(12+x))=0

We add all the numbers together, and all the variables

-(x(x+12))+8^2=0

We add all the numbers together, and all the variables

-(x(x+12))+64=0


We calculate terms in parentheses: -(x(x+12)), so:

x(x+12)

We multiply parentheses

x^2+12x

Back to the equation:

-(x^2+12x)


We get rid of parentheses

-x^2-12x+64=0

We add all the numbers together, and all the variables

-1x^2-12x+64=0

a = -1; b = -12; c = +64;
Δ = b2-4ac
Δ = -122-4·(-1)·64
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20}{2*-1}=\frac{32}{-2}
=-16
$