2y^2+7=61-y^2

Solution for 2y^2+7=61-y^2 equation:

2y^2+7=61-y^2

We move all terms to the left:

2y^2+7-(61-y^2)=0

We get rid of parentheses

2y^2+y^2-61+7=0

We add all the numbers together, and all the variables

3y^2-54=0

a = 3; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·3·(-54)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*3}=\frac{0-18\sqrt{2}}{6}
=-\frac{18\sqrt{2}}{6}
=-3\sqrt{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*3}=\frac{0+18\sqrt{2}}{6}
=\frac{18\sqrt{2}}{6}
=3\sqrt{2}
$