9a2-3a-8=0

Solution for 9a2-3a-8=0 equation:

9a^2-3a-8=0

a = 9; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·9·(-8)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{33}}{2*9}=\frac{3-3\sqrt{33}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{33}}{2*9}=\frac{3+3\sqrt{33}}{18}
$