x^2+5x+9=-x+9

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

x^2+5x+9=-x+9

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2+5x-(-1x+9)+9=0

We get rid of parentheses

x^2+5x+1x-9+9=0

We add all the numbers together, and all the variables

x^2+6x=0

a = 1; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·1·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*1}=\frac{0}{2}
=0
$