5x^2-8x-40=0

Solution for 5x^2-8x-40=0 equation:

5x^2-8x-40=0

a = 5; b = -8; c = -40;
Δ = b2-4ac
Δ = -82-4·5·(-40)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12\sqrt{6}}{2*5}=\frac{8-12\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12\sqrt{6}}{2*5}=\frac{8+12\sqrt{6}}{10}
$