13x^2-10x-5=0

Solution for 13x^2-10x-5=0 equation:

13x^2-10x-5=0

a = 13; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·13·(-5)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{10}}{2*13}=\frac{10-6\sqrt{10}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{10}}{2*13}=\frac{10+6\sqrt{10}}{26}
$