6x2-24x-40=0

Solution for 6x2-24x-40=0 equation:

6x^2-24x-40=0

a = 6; b = -24; c = -40;
Δ = b2-4ac
Δ = -242-4·6·(-40)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{6}}{2*6}=\frac{24-16\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{6}}{2*6}=\frac{24+16\sqrt{6}}{12}
$