13x^2-6x-3=0

Solution for 13x^2-6x-3=0 equation:

13x^2-6x-3=0

a = 13; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·13·(-3)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8\sqrt{3}}{2*13}=\frac{6-8\sqrt{3}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8\sqrt{3}}{2*13}=\frac{6+8\sqrt{3}}{26}
$