11x^2+18x-9=0

Solution for 11x^2+18x-9=0 equation:

11x^2+18x-9=0

a = 11; b = 18; c = -9;
Δ = b2-4ac
Δ = 182-4·11·(-9)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12\sqrt{5}}{2*11}=\frac{-18-12\sqrt{5}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12\sqrt{5}}{2*11}=\frac{-18+12\sqrt{5}}{22}
$