3y(y+5)=2y+15+y

Solution for 3y(y+5)=2y+15+y equation:

3y(y+5)=2y+15+y

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3y^2+12y-15=0

a = 3; b = 12; c = -15;
Δ = b2-4ac
Δ = 122-4·3·(-15)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18}{2*3}=\frac{-30}{6}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18}{2*3}=\frac{6}{6}
=1
$