13x^2-6x-11=0

Solution for 13x^2-6x-11=0 equation:

13x^2-6x-11=0

a = 13; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·13·(-11)
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{38}}{2*13}=\frac{6-4\sqrt{38}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{38}}{2*13}=\frac{6+4\sqrt{38}}{26}
$