3q^2-80q+90=0

Solution for 3q^2-80q+90=0 equation:

3q^2-80q+90=0

a = 3; b = -80; c = +90;
Δ = b2-4ac
Δ = -802-4·3·90
Δ = 5320
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:

$\sqrt{\Delta}=\sqrt{5320}=\sqrt{4*1330}=\sqrt{4}*\sqrt{1330}=2\sqrt{1330}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1330}}{2*3}=\frac{80-2\sqrt{1330}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1330}}{2*3}=\frac{80+2\sqrt{1330}}{6}
$