11x^2-10x-9=0

Solution for 11x^2-10x-9=0 equation:

11x^2-10x-9=0

a = 11; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·11·(-9)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{31}}{2*11}=\frac{10-4\sqrt{31}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{31}}{2*11}=\frac{10+4\sqrt{31}}{22}
$