y(y-14)=62

Solution for y(y-14)=62 equation:

y(y-14)=62

We move all terms to the left:

y(y-14)-(62)=0

We multiply parentheses

y^2-14y-62=0

a = 1; b = -14; c = -62;
Δ = b2-4ac
Δ = -142-4·1·(-62)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{111}}{2*1}=\frac{14-2\sqrt{111}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{111}}{2*1}=\frac{14+2\sqrt{111}}{2}
$