19x2-19x-11=0

Solution for 19x2-19x-11=0 equation:

19x^2-19x-11=0

a = 19; b = -19; c = -11;
Δ = b2-4ac
Δ = -192-4·19·(-11)
Δ = 1197
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:

$\sqrt{\Delta}=\sqrt{1197}=\sqrt{9*133}=\sqrt{9}*\sqrt{133}=3\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{133}}{2*19}=\frac{19-3\sqrt{133}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{133}}{2*19}=\frac{19+3\sqrt{133}}{38}
$