y(y+6)=6

Solution for y(y+6)=6 equation:

y(y+6)=6

We move all terms to the left:

y(y+6)-(6)=0

We multiply parentheses

y^2+6y-6=0

a = 1; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·1·(-6)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*1}=\frac{-6-2\sqrt{15}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*1}=\frac{-6+2\sqrt{15}}{2}
$