8y=y(y+11)

Solution for 8y=y(y+11) equation:

8y=y(y+11)

We move all terms to the left:

8y-(y(y+11))=0


We calculate terms in parentheses: -(y(y+11)), so:

y(y+11)

We multiply parentheses

y^2+11y

Back to the equation:

-(y^2+11y)


We get rid of parentheses

-y^2+8y-11y=0

We add all the numbers together, and all the variables

-1y^2-3y=0

a = -1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-1)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-1}=\frac{0}{-2}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-1}=\frac{6}{-2}
=-3
$