6(y-11)y=-6

Solution for 6(y-11)y=-6 equation:

6(y-11)y=-6

We move all terms to the left:

6(y-11)y-(-6)=0

We add all the numbers together, and all the variables

6(y-11)y+6=0

We multiply parentheses

6y^2-66y+6=0

a = 6; b = -66; c = +6;
Δ = b2-4ac
Δ = -662-4·6·6
Δ = 4212
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:

$\sqrt{\Delta}=\sqrt{4212}=\sqrt{324*13}=\sqrt{324}*\sqrt{13}=18\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-18\sqrt{13}}{2*6}=\frac{66-18\sqrt{13}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+18\sqrt{13}}{2*6}=\frac{66+18\sqrt{13}}{12}
$