x^2=12(x+9)

Solution for x^2=12(x+9) equation:

x^2=12(x+9)

We move all terms to the left:

x^2-(12(x+9))=0


We calculate terms in parentheses: -(12(x+9)), so:

12(x+9)

We multiply parentheses

12x+108

Back to the equation:

-(12x+108)


We get rid of parentheses

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