y^2+31=8y-4+180

Solution for y^2+31=8y-4+180 equation:

y^2+31=8y-4+180

We move all terms to the left:

y^2+31-(8y-4+180)=0

We add all the numbers together, and all the variables

y^2-(8y+176)+31=0

We get rid of parentheses

y^2-8y-176+31=0

We add all the numbers together, and all the variables

y^2-8y-145=0

a = 1; b = -8; c = -145;
Δ = b2-4ac
Δ = -82-4·1·(-145)
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{161}}{2*1}=\frac{8-2\sqrt{161}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{161}}{2*1}=\frac{8+2\sqrt{161}}{2}
$