5x^2-2x-40=0

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

5x^2-2x-40=0

a = 5; b = -2; c = -40;
Δ = b2-4ac
Δ = -22-4·5·(-40)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{201}}{2*5}=\frac{2-2\sqrt{201}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{201}}{2*5}=\frac{2+2\sqrt{201}}{10}
$