9a2-8a-24=0

Solution for 9a2-8a-24=0 equation:

9a^2-8a-24=0

a = 9; b = -8; c = -24;
Δ = b2-4ac
Δ = -82-4·9·(-24)
Δ = 928
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{58}}{2*9}=\frac{8-4\sqrt{58}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{58}}{2*9}=\frac{8+4\sqrt{58}}{18}
$