(x+6)(x-6)=-3x

Solution for (x+6)(x-6)=-3x equation:

(x+6)(x-6)=-3x

We move all terms to the left:

(x+6)(x-6)-(-3x)=0

We use the square of the difference formula

x^2-(-3x)-36=0

We get rid of parentheses

x^2+3x-36=0

a = 1; b = 3; c = -36;
Δ = b2-4ac
Δ = 32-4·1·(-36)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{17}}{2*1}=\frac{-3-3\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{17}}{2*1}=\frac{-3+3\sqrt{17}}{2}
$