3y^2+8y-9=0

Solution for 3y^2+8y-9=0 equation:

3y^2+8y-9=0

a = 3; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·3·(-9)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{43}}{2*3}=\frac{-8-2\sqrt{43}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{43}}{2*3}=\frac{-8+2\sqrt{43}}{6}
$