6y^2-30y+37=0

Solution for 6y^2-30y+37=0 equation:

6y^2-30y+37=0

a = 6; b = -30; c = +37;
Δ = b2-4ac
Δ = -302-4·6·37
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{3}}{2*6}=\frac{30-2\sqrt{3}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{3}}{2*6}=\frac{30+2\sqrt{3}}{12}
$