18y-6y=11y(y+2)+y

Solution for 18y-6y=11y(y+2)+y equation:

18y-6y=11y(y+2)+y

We move all terms to the left:

18y-6y-(11y(y+2)+y)=0

We add all the numbers together, and all the variables

12y-(11y(y+2)+y)=0


We calculate terms in parentheses: -(11y(y+2)+y), so:

11y(y+2)+y

We add all the numbers together, and all the variables

y+11y(y+2)

We multiply parentheses

11y^2+y+22y

We add all the numbers together, and all the variables

11y^2+23y

Back to the equation:

-(11y^2+23y)


We get rid of parentheses

-11y^2+12y-23y=0

We add all the numbers together, and all the variables

-11y^2-11y=0

a = -11; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-11)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-11}=\frac{0}{-22}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-11}=\frac{22}{-22}
=-1
$