40x^2-24x-72=0

Solution for 40x^2-24x-72=0 equation:

40x^2-24x-72=0

a = 40; b = -24; c = -72;
Δ = b2-4ac
Δ = -242-4·40·(-72)
Δ = 12096
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:

$\sqrt{\Delta}=\sqrt{12096}=\sqrt{576*21}=\sqrt{576}*\sqrt{21}=24\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{21}}{2*40}=\frac{24-24\sqrt{21}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{21}}{2*40}=\frac{24+24\sqrt{21}}{80}
$