7y^2-6=31

Solution for 7y^2-6=31 equation:

7y^2-6=31

We move all terms to the left:

7y^2-6-(31)=0

We add all the numbers together, and all the variables

7y^2-37=0

a = 7; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·7·(-37)
Δ = 1036
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:

$\sqrt{\Delta}=\sqrt{1036}=\sqrt{4*259}=\sqrt{4}*\sqrt{259}=2\sqrt{259}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{259}}{2*7}=\frac{0-2\sqrt{259}}{14}
=-\frac{2\sqrt{259}}{14}
=-\frac{\sqrt{259}}{7}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{259}}{2*7}=\frac{0+2\sqrt{259}}{14}
=\frac{2\sqrt{259}}{14}
=\frac{\sqrt{259}}{7}
$