4y(5y-3)=-15y+9

Solution for 4y(5y-3)=-15y+9 equation:

4y(5y-3)=-15y+9

We move all terms to the left:

4y(5y-3)-(-15y+9)=0

We multiply parentheses

20y^2-12y-(-15y+9)=0

We get rid of parentheses

20y^2-12y+15y-9=0

We add all the numbers together, and all the variables

20y^2+3y-9=0

a = 20; b = 3; c = -9;
Δ = b2-4ac
Δ = 32-4·20·(-9)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-27}{2*20}=\frac{-30}{40}
=-3/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+27}{2*20}=\frac{24}{40}
=3/5
$