54x^2-24x-96=0

Solution for 54x^2-24x-96=0 equation:

54x^2-24x-96=0

a = 54; b = -24; c = -96;
Δ = b2-4ac
Δ = -242-4·54·(-96)
Δ = 21312
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:

$\sqrt{\Delta}=\sqrt{21312}=\sqrt{576*37}=\sqrt{576}*\sqrt{37}=24\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{37}}{2*54}=\frac{24-24\sqrt{37}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{37}}{2*54}=\frac{24+24\sqrt{37}}{108}
$