24x^2-72x-54=0

Solution for 24x^2-72x-54=0 equation:

24x^2-72x-54=0

a = 24; b = -72; c = -54;
Δ = b2-4ac
Δ = -722-4·24·(-54)
Δ = 10368
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:

$\sqrt{\Delta}=\sqrt{10368}=\sqrt{5184*2}=\sqrt{5184}*\sqrt{2}=72\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72\sqrt{2}}{2*24}=\frac{72-72\sqrt{2}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72\sqrt{2}}{2*24}=\frac{72+72\sqrt{2}}{48}
$