x^2=12x+9

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

x^2=12x+9

We move all terms to the left:

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

We get rid of parentheses

x^2-12x-9=0

a = 1; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·1·(-9)
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{5}}{2*1}=\frac{12-6\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{5}}{2*1}=\frac{12+6\sqrt{5}}{2}
$