3(y-3)5y=-15

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

3(y-3)5y=-15

We move all terms to the left:

3(y-3)5y-(-15)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

15y^2-45y+15=0

a = 15; b = -45; c = +15;
Δ = b2-4ac
Δ = -452-4·15·15
Δ = 1125
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:

$\sqrt{\Delta}=\sqrt{1125}=\sqrt{225*5}=\sqrt{225}*\sqrt{5}=15\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-15\sqrt{5}}{2*15}=\frac{45-15\sqrt{5}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+15\sqrt{5}}{2*15}=\frac{45+15\sqrt{5}}{30}
$