13x^2-14x-5=0

Solution for 13x^2-14x-5=0 equation:

13x^2-14x-5=0

a = 13; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·13·(-5)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{114}}{2*13}=\frac{14-2\sqrt{114}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{114}}{2*13}=\frac{14+2\sqrt{114}}{26}
$