5y+7+y^2+31=180

Solution for 5y+7+y^2+31=180 equation:

5y+7+y^2+31=180

We move all terms to the left:

5y+7+y^2+31-(180)=0

We add all the numbers together, and all the variables

y^2+5y-142=0

a = 1; b = 5; c = -142;
Δ = b2-4ac
Δ = 52-4·1·(-142)
Δ = 593
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{-(5)-\sqrt{593}}{2*1}=\frac{-5-\sqrt{593}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{593}}{2*1}=\frac{-5+\sqrt{593}}{2}
$