11x^2+x-19=0

Solution for 11x^2+x-19=0 equation:

11x^2+x-19=0

a = 11; b = 1; c = -19;
Δ = b2-4ac
Δ = 12-4·11·(-19)
Δ = 837
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:

$\sqrt{\Delta}=\sqrt{837}=\sqrt{9*93}=\sqrt{9}*\sqrt{93}=3\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{93}}{2*11}=\frac{-1-3\sqrt{93}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{93}}{2*11}=\frac{-1+3\sqrt{93}}{22}
$