y^2-2y=37

Solution for y^2-2y=37 equation:

y^2-2y=37

We move all terms to the left:

y^2-2y-(37)=0

a = 1; b = -2; c = -37;
Δ = b2-4ac
Δ = -22-4·1·(-37)
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{38}}{2*1}=\frac{2-2\sqrt{38}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{38}}{2*1}=\frac{2+2\sqrt{38}}{2}
$