11x^2=-9x-1

Solution for 11x^2=-9x-1 equation:

11x^2=-9x-1

We move all terms to the left:

11x^2-(-9x-1)=0

We get rid of parentheses

11x^2+9x+1=0

a = 11; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·11·1
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{37}}{2*11}=\frac{-9-\sqrt{37}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{37}}{2*11}=\frac{-9+\sqrt{37}}{22}
$