3y2-180y+60=0

Solution for 3y2-180y+60=0 equation:

3y^2-180y+60=0

a = 3; b = -180; c = +60;
Δ = b2-4ac
Δ = -1802-4·3·60
Δ = 31680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{31680}=\sqrt{576*55}=\sqrt{576}*\sqrt{55}=24\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-24\sqrt{55}}{2*3}=\frac{180-24\sqrt{55}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+24\sqrt{55}}{2*3}=\frac{180+24\sqrt{55}}{6}
$