y^2-2y=19

Solution for y^2-2y=19 equation:

y^2-2y=19

We move all terms to the left:

y^2-2y-(19)=0

a = 1; b = -2; c = -19;
Δ = b2-4ac
Δ = -22-4·1·(-19)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{5}}{2*1}=\frac{2-4\sqrt{5}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{5}}{2*1}=\frac{2+4\sqrt{5}}{2}
$