5x^2-16x-13=0

Solution for 5x^2-16x-13=0 equation:

5x^2-16x-13=0

a = 5; b = -16; c = -13;
Δ = b2-4ac
Δ = -162-4·5·(-13)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{129}}{2*5}=\frac{16-2\sqrt{129}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{129}}{2*5}=\frac{16+2\sqrt{129}}{10}
$