3y^2+8y-9=24

Solution for 3y^2+8y-9=24 equation:

3y^2+8y-9=24

We move all terms to the left:

3y^2+8y-9-(24)=0

We add all the numbers together, and all the variables

3y^2+8y-33=0

a = 3; b = 8; c = -33;
Δ = b2-4ac
Δ = 82-4·3·(-33)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{115}}{2*3}=\frac{-8-2\sqrt{115}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{115}}{2*3}=\frac{-8+2\sqrt{115}}{6}
$