14x2-x-11=0

Solution for 14x2-x-11=0 equation:

14x^2-x-11=0

We add all the numbers together, and all the variables

14x^2-1x-11=0

a = 14; b = -1; c = -11;
Δ = b2-4ac
Δ = -12-4·14·(-11)
Δ = 617
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{617}}{2*14}=\frac{1-\sqrt{617}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{617}}{2*14}=\frac{1+\sqrt{617}}{28}
$