-5y(y-3)=9

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

-5y(y-3)=9

We move all terms to the left:

-5y(y-3)-(9)=0

We multiply parentheses

-5y^2+15y-9=0

a = -5; b = 15; c = -9;
Δ = b2-4ac
Δ = 152-4·(-5)·(-9)
Δ = 45
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{5}}{2*-5}=\frac{-15-3\sqrt{5}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{5}}{2*-5}=\frac{-15+3\sqrt{5}}{-10}
$