(3y+9)(y-2)=24

Solution for (3y+9)(y-2)=24 equation:

(3y+9)(y-2)=24

We move all terms to the left:

(3y+9)(y-2)-(24)=0

We multiply parentheses ..

(+3y^2-6y+9y-18)-24=0

We get rid of parentheses

3y^2-6y+9y-18-24=0

We add all the numbers together, and all the variables

3y^2+3y-42=0

a = 3; b = 3; c = -42;
Δ = b2-4ac
Δ = 32-4·3·(-42)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{57}}{2*3}=\frac{-3-3\sqrt{57}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{57}}{2*3}=\frac{-3+3\sqrt{57}}{6}
$