9x(x+8)-6=66

Solution for 9x(x+8)-6=66 equation:

9x(x+8)-6=66

We move all terms to the left:

9x(x+8)-6-(66)=0

We add all the numbers together, and all the variables

9x(x+8)-72=0

We multiply parentheses

9x^2+72x-72=0

a = 9; b = 72; c = -72;
Δ = b2-4ac
Δ = 722-4·9·(-72)
Δ = 7776
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:

$\sqrt{\Delta}=\sqrt{7776}=\sqrt{1296*6}=\sqrt{1296}*\sqrt{6}=36\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-36\sqrt{6}}{2*9}=\frac{-72-36\sqrt{6}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+36\sqrt{6}}{2*9}=\frac{-72+36\sqrt{6}}{18}
$