a^2-12a-15=-6

Solution for a^2-12a-15=-6 equation:

a^2-12a-15=-6

We move all terms to the left:

a^2-12a-15-(-6)=0

We add all the numbers together, and all the variables

a^2-12a-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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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