9a^2+6a-11=0

Solution for 9a^2+6a-11=0 equation:

9a^2+6a-11=0

a = 9; b = 6; c = -11;
Δ = b2-4ac
Δ = 62-4·9·(-11)
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12\sqrt{3}}{2*9}=\frac{-6-12\sqrt{3}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12\sqrt{3}}{2*9}=\frac{-6+12\sqrt{3}}{18}
$