6x^2-40x-24=0

Solution for 6x^2-40x-24=0 equation:

6x^2-40x-24=0

a = 6; b = -40; c = -24;
Δ = b2-4ac
Δ = -402-4·6·(-24)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{34}}{2*6}=\frac{40-8\sqrt{34}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{34}}{2*6}=\frac{40+8\sqrt{34}}{12}
$