y^2-5y+20=31

Solution for y^2-5y+20=31 equation:

y^2-5y+20=31

We move all terms to the left:

y^2-5y+20-(31)=0

We add all the numbers together, and all the variables

y^2-5y-11=0

a = 1; b = -5; c = -11;
Δ = b2-4ac
Δ = -52-4·1·(-11)
Δ = 69
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{69}}{2*1}=\frac{5-\sqrt{69}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{69}}{2*1}=\frac{5+\sqrt{69}}{2}
$