5y^2-30y-48=0

Solution for 5y^2-30y-48=0 equation:

5y^2-30y-48=0

a = 5; b = -30; c = -48;
Δ = b2-4ac
Δ = -302-4·5·(-48)
Δ = 1860
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:

$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{465}}{2*5}=\frac{30-2\sqrt{465}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{465}}{2*5}=\frac{30+2\sqrt{465}}{10}
$