5x2-19x-13=0

Solution for 5x2-19x-13=0 equation:

5x^2-19x-13=0

a = 5; b = -19; c = -13;
Δ = b2-4ac
Δ = -192-4·5·(-13)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{69}}{2*5}=\frac{19-3\sqrt{69}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{69}}{2*5}=\frac{19+3\sqrt{69}}{10}
$