9q^2-4q-32=0

Solution for 9q^2-4q-32=0 equation:

9q^2-4q-32=0

a = 9; b = -4; c = -32;
Δ = b2-4ac
Δ = -42-4·9·(-32)
Δ = 1168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{73}}{2*9}=\frac{4-4\sqrt{73}}{18}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{73}}{2*9}=\frac{4+4\sqrt{73}}{18}
$