31y^2-48=y

Solution for 31y^2-48=y equation:

31y^2-48=y

We move all terms to the left:

31y^2-48-(y)=0

We add all the numbers together, and all the variables

31y^2-1y-48=0

a = 31; b = -1; c = -48;
Δ = b2-4ac
Δ = -12-4·31·(-48)
Δ = 5953
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{5953}}{2*31}=\frac{1-\sqrt{5953}}{62}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5953}}{2*31}=\frac{1+\sqrt{5953}}{62}
$