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

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

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

We add all the numbers together, and all the variables

9x^2-9x-72=0

a = 9; b = -9; c = -72;
Δ = b2-4ac
Δ = -92-4·9·(-72)
Δ = 2673
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:

$\sqrt{\Delta}=\sqrt{2673}=\sqrt{81*33}=\sqrt{81}*\sqrt{33}=9\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{33}}{2*9}=\frac{9-9\sqrt{33}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{33}}{2*9}=\frac{9+9\sqrt{33}}{18}
$