90-2q-3q^2=0

Solution for 90-2q-3q^2=0 equation:

90-2q-3q^2=0

a = -3; b = -2; c = +90;
Δ = b2-4ac
Δ = -22-4·(-3)·90
Δ = 1084
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:

$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{271}}{2*-3}=\frac{2-2\sqrt{271}}{-6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{271}}{2*-3}=\frac{2+2\sqrt{271}}{-6}
$