-9(-8x-3)x=8

Solution for -9(-8x-3)x=8 equation:

-9(-8x-3)x=8

We move all terms to the left:

-9(-8x-3)x-(8)=0

We multiply parentheses

72x^2+27x-8=0

a = 72; b = 27; c = -8;
Δ = b2-4ac
Δ = 272-4·72·(-8)
Δ = 3033
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:

$\sqrt{\Delta}=\sqrt{3033}=\sqrt{9*337}=\sqrt{9}*\sqrt{337}=3\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{337}}{2*72}=\frac{-27-3\sqrt{337}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{337}}{2*72}=\frac{-27+3\sqrt{337}}{144}
$