5y(3y+9)=12

Solution for 5y(3y+9)=12 equation:

5y(3y+9)=12

We move all terms to the left:

5y(3y+9)-(12)=0

We multiply parentheses

15y^2+45y-12=0

a = 15; b = 45; c = -12;
Δ = b2-4ac
Δ = 452-4·15·(-12)
Δ = 2745
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:

$\sqrt{\Delta}=\sqrt{2745}=\sqrt{9*305}=\sqrt{9}*\sqrt{305}=3\sqrt{305}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{305}}{2*15}=\frac{-45-3\sqrt{305}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{305}}{2*15}=\frac{-45+3\sqrt{305}}{30}
$