5y^2-6y-48=0

Solution for 5y^2-6y-48=0 equation:

5y^2-6y-48=0

a = 5; b = -6; c = -48;
Δ = b2-4ac
Δ = -62-4·5·(-48)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{249}}{2*5}=\frac{6-2\sqrt{249}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{249}}{2*5}=\frac{6+2\sqrt{249}}{10}
$