6y(y+11)=5y

Solution for 6y(y+11)=5y equation:

6y(y+11)=5y

We move all terms to the left:

6y(y+11)-(5y)=0

We add all the numbers together, and all the variables

-5y+6y(y+11)=0

We multiply parentheses

6y^2-5y+66y=0

We add all the numbers together, and all the variables

6y^2+61y=0

a = 6; b = 61; c = 0;
Δ = b2-4ac
Δ = 612-4·6·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-61}{2*6}=\frac{-122}{12}
=-10+1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+61}{2*6}=\frac{0}{12}
=0
$