5y^2+24y-24=0

Solution for 5y^2+24y-24=0 equation:

5y^2+24y-24=0

a = 5; b = 24; c = -24;
Δ = b2-4ac
Δ = 242-4·5·(-24)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{66}}{2*5}=\frac{-24-4\sqrt{66}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{66}}{2*5}=\frac{-24+4\sqrt{66}}{10}
$