11x^2+2x-92=0

Solution for 11x^2+2x-92=0 equation:

11x^2+2x-92=0

a = 11; b = 2; c = -92;
Δ = b2-4ac
Δ = 22-4·11·(-92)
Δ = 4052
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:

$\sqrt{\Delta}=\sqrt{4052}=\sqrt{4*1013}=\sqrt{4}*\sqrt{1013}=2\sqrt{1013}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1013}}{2*11}=\frac{-2-2\sqrt{1013}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1013}}{2*11}=\frac{-2+2\sqrt{1013}}{22}
$