5+9x=-3x^2

Solution for 5+9x=-3x^2 equation:

5+9x=-3x^2

We move all terms to the left:

5+9x-(-3x^2)=0

We get rid of parentheses

3x^2+9x+5=0

a = 3; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·3·5
Δ = 21
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{21}}{2*3}=\frac{-9-\sqrt{21}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{21}}{2*3}=\frac{-9+\sqrt{21}}{6}
$