11x^2+14x-77=0

Solution for 11x^2+14x-77=0 equation:

11x^2+14x-77=0

a = 11; b = 14; c = -77;
Δ = b2-4ac
Δ = 142-4·11·(-77)
Δ = 3584
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:

$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-16\sqrt{14}}{2*11}=\frac{-14-16\sqrt{14}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+16\sqrt{14}}{2*11}=\frac{-14+16\sqrt{14}}{22}
$