24x^2-54x-540=0

Solution for 24x^2-54x-540=0 equation:

24x^2-54x-540=0

a = 24; b = -54; c = -540;
Δ = b2-4ac
Δ = -542-4·24·(-540)
Δ = 54756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{54756}=234$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-234}{2*24}=\frac{-180}{48}
=-3+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+234}{2*24}=\frac{288}{48}
=6
$