5x^2-20x-13=0

Solution for 5x^2-20x-13=0 equation:

5x^2-20x-13=0

a = 5; b = -20; c = -13;
Δ = b2-4ac
Δ = -202-4·5·(-13)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{165}}{2*5}=\frac{20-2\sqrt{165}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{165}}{2*5}=\frac{20+2\sqrt{165}}{10}
$