30y^2-6=31y

Solution for 30y^2-6=31y equation:

30y^2-6=31y

We move all terms to the left:

30y^2-6-(31y)=0

a = 30; b = -31; c = -6;
Δ = b2-4ac
Δ = -312-4·30·(-6)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-41}{2*30}=\frac{-10}{60}
=-1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+41}{2*30}=\frac{72}{60}
=1+1/5
$