3y(y-4)+2y=15

Solution for 3y(y-4)+2y=15 equation:

3y(y-4)+2y=15

We move all terms to the left:

3y(y-4)+2y-(15)=0

We add all the numbers together, and all the variables

2y+3y(y-4)-15=0

We multiply parentheses

3y^2+2y-12y-15=0

We add all the numbers together, and all the variables

3y^2-10y-15=0

a = 3; b = -10; c = -15;
Δ = b2-4ac
Δ = -102-4·3·(-15)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{70}}{2*3}=\frac{10-2\sqrt{70}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{70}}{2*3}=\frac{10+2\sqrt{70}}{6}
$