15(-y+3)31y=-3

Solution for 15(-y+3)31y=-3 equation:

15(-y+3)31y=-3

We move all terms to the left:

15(-y+3)31y-(-3)=0

We add all the numbers together, and all the variables

15(-1y+3)31y-(-3)=0

We add all the numbers together, and all the variables

15(-1y+3)31y+3=0

We multiply parentheses

-465y^2+1395y+3=0

a = -465; b = 1395; c = +3;
Δ = b2-4ac
Δ = 13952-4·(-465)·3
Δ = 1951605
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:

$\sqrt{\Delta}=\sqrt{1951605}=\sqrt{9*216845}=\sqrt{9}*\sqrt{216845}=3\sqrt{216845}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1395)-3\sqrt{216845}}{2*-465}=\frac{-1395-3\sqrt{216845}}{-930}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1395)+3\sqrt{216845}}{2*-465}=\frac{-1395+3\sqrt{216845}}{-930}
$