y2+22=382y

Solution for y2+22=382y equation:

y2+22=382y

We move all terms to the left:

y2+22-(382y)=0

We add all the numbers together, and all the variables

y^2-382y+22=0

a = 1; b = -382; c = +22;
Δ = b2-4ac
Δ = -3822-4·1·22
Δ = 145836
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:

$\sqrt{\Delta}=\sqrt{145836}=\sqrt{36*4051}=\sqrt{36}*\sqrt{4051}=6\sqrt{4051}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-382)-6\sqrt{4051}}{2*1}=\frac{382-6\sqrt{4051}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-382)+6\sqrt{4051}}{2*1}=\frac{382+6\sqrt{4051}}{2}
$