y(2y+4)=9y

Solution for y(2y+4)=9y equation:

y(2y+4)=9y

We move all terms to the left:

y(2y+4)-(9y)=0

We add all the numbers together, and all the variables

-9y+y(2y+4)=0

We multiply parentheses

2y^2-9y+4y=0

We add all the numbers together, and all the variables

2y^2-5y=0

a = 2; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·2·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*2}=\frac{0}{4}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*2}=\frac{10}{4}
=2+1/2
$