6y^2+30y-24=0

Solution for 6y^2+30y-24=0 equation:

6y^2+30y-24=0

a = 6; b = 30; c = -24;
Δ = b2-4ac
Δ = 302-4·6·(-24)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{41}}{2*6}=\frac{-30-6\sqrt{41}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{41}}{2*6}=\frac{-30+6\sqrt{41}}{12}
$