1.5q^2-60q+200=0

Solution for 1.5q^2-60q+200=0 equation:

1.5q^2-60q+200=0

a = 1.5; b = -60; c = +200;
Δ = b2-4ac
Δ = -602-4·1.5·200
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{6}}{2*1.5}=\frac{60-20\sqrt{6}}{3}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{6}}{2*1.5}=\frac{60+20\sqrt{6}}{3}
$