X2-12x=-9

Solution for X2-12x=-9 equation:

X2-12X=-9

We move all terms to the left:

X2-12X-(-9)=0

We add all the numbers together, and all the variables

X^2-12X+9=0

a = 1; b = -12; c = +9;
Δ = b2-4ac
Δ = -122-4·1·9
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{3}}{2*1}=\frac{12-6\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{3}}{2*1}=\frac{12+6\sqrt{3}}{2}
$