24x^2-18x-20=0

Solution for 24x^2-18x-20=0 equation:

24x^2-18x-20=0

a = 24; b = -18; c = -20;
Δ = b2-4ac
Δ = -182-4·24·(-20)
Δ = 2244
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:

$\sqrt{\Delta}=\sqrt{2244}=\sqrt{4*561}=\sqrt{4}*\sqrt{561}=2\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{561}}{2*24}=\frac{18-2\sqrt{561}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{561}}{2*24}=\frac{18+2\sqrt{561}}{48}
$