-8x^2-9x+72=0

Solution for -8x^2-9x+72=0 equation:

-8x^2-9x+72=0

a = -8; b = -9; c = +72;
Δ = b2-4ac
Δ = -92-4·(-8)·72
Δ = 2385
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:

$\sqrt{\Delta}=\sqrt{2385}=\sqrt{9*265}=\sqrt{9}*\sqrt{265}=3\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{265}}{2*-8}=\frac{9-3\sqrt{265}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{265}}{2*-8}=\frac{9+3\sqrt{265}}{-16}
$