(y-11)(6y+3)=0

Solution for (y-11)(6y+3)=0 equation:

(y-11)(6y+3)=0

We multiply parentheses ..

(+6y^2+3y-66y-33)=0

We get rid of parentheses

6y^2+3y-66y-33=0

We add all the numbers together, and all the variables

6y^2-63y-33=0

a = 6; b = -63; c = -33;
Δ = b2-4ac
Δ = -632-4·6·(-33)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-69}{2*6}=\frac{-6}{12}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+69}{2*6}=\frac{132}{12}
=11
$