5x^2-16x-40=0

Solution for 5x^2-16x-40=0 equation:

5x^2-16x-40=0

a = 5; b = -16; c = -40;
Δ = b2-4ac
Δ = -162-4·5·(-40)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{66}}{2*5}=\frac{16-4\sqrt{66}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{66}}{2*5}=\frac{16+4\sqrt{66}}{10}
$