11x+1=-9x^2

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

11x+1=-9x^2

We move all terms to the left:

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

We get rid of parentheses

9x^2+11x+1=0

a = 9; b = 11; c = +1;
Δ = b2-4ac
Δ = 112-4·9·1
Δ = 85
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{-(11)-\sqrt{85}}{2*9}=\frac{-11-\sqrt{85}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{85}}{2*9}=\frac{-11+\sqrt{85}}{18}
$