(2y^2+7)+(61-y^2)+63=180

Solution for (2y^2+7)+(61-y^2)+63=180 equation:

(2y^2+7)+(61-y^2)+63=180

We move all terms to the left:

(2y^2+7)+(61-y^2)+63-(180)=0

We add all the numbers together, and all the variables

(61-y^2)+(2y^2+7)-117=0

We get rid of parentheses

-y^2+2y^2+61+7-117=0

We add all the numbers together, and all the variables

y^2-49=0

a = 1; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·1·(-49)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14}{2*1}=\frac{-14}{2}
=-7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14}{2*1}=\frac{14}{2}
=7
$