11x^2+6x-7=0

Solution for 11x^2+6x-7=0 equation:

11x^2+6x-7=0

a = 11; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·11·(-7)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{86}}{2*11}=\frac{-6-2\sqrt{86}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{86}}{2*11}=\frac{-6+2\sqrt{86}}{22}
$