y^2-22y=112

Solution for y^2-22y=112 equation:

y^2-22y=112

We move all terms to the left:

y^2-22y-(112)=0

a = 1; b = -22; c = -112;
Δ = b2-4ac
Δ = -222-4·1·(-112)
Δ = 932
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:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{233}}{2*1}=\frac{22-2\sqrt{233}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{233}}{2*1}=\frac{22+2\sqrt{233}}{2}
$