108=x(x-12)

Solution for 108=x(x-12) equation:

108=x(x-12)

We move all terms to the left:

108-(x(x-12))=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+108=0

We add all the numbers together, and all the variables

-1x^2+12x+108=0

a = -1; b = 12; c = +108;
Δ = b2-4ac
Δ = 122-4·(-1)·108
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*-1}=\frac{-36}{-2}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*-1}=\frac{12}{-2}
=-6
$