48r^2-120r-48=0

Solution for 48r^2-120r-48=0 equation:

48r^2-120r-48=0

a = 48; b = -120; c = -48;
Δ = b2-4ac
Δ = -1202-4·48·(-48)
Δ = 23616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{23616}=\sqrt{576*41}=\sqrt{576}*\sqrt{41}=24\sqrt{41}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-24\sqrt{41}}{2*48}=\frac{120-24\sqrt{41}}{96}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+24\sqrt{41}}{2*48}=\frac{120+24\sqrt{41}}{96}
$