3y^2+9y=8

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

3y^2+9y=8

We move all terms to the left:

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

a = 3; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·3·(-8)
Δ = 177
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{-(9)-\sqrt{177}}{2*3}=\frac{-9-\sqrt{177}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{177}}{2*3}=\frac{-9+\sqrt{177}}{6}
$