3(y+8)=2(y-6)y=30

Solution for 3(y+8)=2(y-6)y=30 equation:

3(y+8)=2(y-6)y=30

We move all terms to the left:

3(y+8)-(2(y-6)y)=0

We multiply parentheses

3y-(2(y-6)y)+24=0


We calculate terms in parentheses: -(2(y-6)y), so:

2(y-6)y

We multiply parentheses

2y^2-12y

Back to the equation:

-(2y^2-12y)


We get rid of parentheses

-2y^2+3y+12y+24=0

We add all the numbers together, and all the variables

-2y^2+15y+24=0

a = -2; b = 15; c = +24;
Δ = b2-4ac
Δ = 152-4·(-2)·24
Δ = 417
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{417}}{2*-2}=\frac{-15-\sqrt{417}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{417}}{2*-2}=\frac{-15+\sqrt{417}}{-4}
$