5y(2y-3)=-6y+9

Solution for 5y(2y-3)=-6y+9 equation:

5y(2y-3)=-6y+9

We move all terms to the left:

5y(2y-3)-(-6y+9)=0

We multiply parentheses

10y^2-15y-(-6y+9)=0

We get rid of parentheses

10y^2-15y+6y-9=0

We add all the numbers together, and all the variables

10y^2-9y-9=0

a = 10; b = -9; c = -9;
Δ = b2-4ac
Δ = -92-4·10·(-9)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-21}{2*10}=\frac{-12}{20}
=-3/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+21}{2*10}=\frac{30}{20}
=1+1/2
$