24x^2+54x-120=0

Solution for 24x^2+54x-120=0 equation:

24x^2+54x-120=0

a = 24; b = 54; c = -120;
Δ = b2-4ac
Δ = 542-4·24·(-120)
Δ = 14436
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14436}=\sqrt{36*401}=\sqrt{36}*\sqrt{401}=6\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{401}}{2*24}=\frac{-54-6\sqrt{401}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{401}}{2*24}=\frac{-54+6\sqrt{401}}{48}
$