4y(y-5)=9y

Solution for 4y(y-5)=9y equation:

4y(y-5)=9y

We move all terms to the left:

4y(y-5)-(9y)=0

We add all the numbers together, and all the variables

-9y+4y(y-5)=0

We multiply parentheses

4y^2-9y-20y=0

We add all the numbers together, and all the variables

4y^2-29y=0

a = 4; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·4·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*4}=\frac{0}{8}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*4}=\frac{58}{8}
=7+1/4
$