6y^2-30y+30=0

Solution for 6y^2-30y+30=0 equation:

6y^2-30y+30=0

a = 6; b = -30; c = +30;
Δ = b2-4ac
Δ = -302-4·6·30
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{5}}{2*6}=\frac{30-6\sqrt{5}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{5}}{2*6}=\frac{30+6\sqrt{5}}{12}
$