3y^2-8y-15=0

Solution for 3y^2-8y-15=0 equation:

3y^2-8y-15=0

a = 3; b = -8; c = -15;
Δ = b2-4ac
Δ = -82-4·3·(-15)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{61}}{2*3}=\frac{8-2\sqrt{61}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{61}}{2*3}=\frac{8+2\sqrt{61}}{6}
$