-8x(x-9)-7=65

Solution for -8x(x-9)-7=65 equation:

-8x(x-9)-7=65

We move all terms to the left:

-8x(x-9)-7-(65)=0

We add all the numbers together, and all the variables

-8x(x-9)-72=0

We multiply parentheses

-8x^2+72x-72=0

a = -8; b = 72; c = -72;
Δ = b2-4ac
Δ = 722-4·(-8)·(-72)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-24\sqrt{5}}{2*-8}=\frac{-72-24\sqrt{5}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+24\sqrt{5}}{2*-8}=\frac{-72+24\sqrt{5}}{-16}
$