2y^2-15-5y=y2-3y

Solution for 2y^2-15-5y=y2-3y equation:

2y^2-15-5y=y2-3y

We move all terms to the left:

2y^2-15-5y-(y2-3y)=0

We add all the numbers together, and all the variables

2y^2-(+y^2-3y)-5y-15=0

We get rid of parentheses

2y^2-y^2+3y-5y-15=0

We add all the numbers together, and all the variables

y^2-2y-15=0

a = 1; b = -2; c = -15;
Δ = b2-4ac
Δ = -22-4·1·(-15)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8}{2*1}=\frac{-6}{2}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*1}=\frac{10}{2}
=5
$