24x^2-48x-18=0

Solution for 24x^2-48x-18=0 equation:

24x^2-48x-18=0

a = 24; b = -48; c = -18;
Δ = b2-4ac
Δ = -482-4·24·(-18)
Δ = 4032
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:

$\sqrt{\Delta}=\sqrt{4032}=\sqrt{576*7}=\sqrt{576}*\sqrt{7}=24\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{7}}{2*24}=\frac{48-24\sqrt{7}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{7}}{2*24}=\frac{48+24\sqrt{7}}{48}
$