2y2+6y-24=0

Solution for 2y2+6y-24=0 equation:

2y^2+6y-24=0

a = 2; b = 6; c = -24;
Δ = b2-4ac
Δ = 62-4·2·(-24)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{57}}{2*2}=\frac{-6-2\sqrt{57}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{57}}{2*2}=\frac{-6+2\sqrt{57}}{4}
$