9x^2+24x-32=0

Solution for 9x^2+24x-32=0 equation:

9x^2+24x-32=0

a = 9; b = 24; c = -32;
Δ = b2-4ac
Δ = 242-4·9·(-32)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{3}}{2*9}=\frac{-24-24\sqrt{3}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{3}}{2*9}=\frac{-24+24\sqrt{3}}{18}
$