(-x)=x^2+9x

Solution for (-x)=x^2+9x equation:

(-x)=x^2+9x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-10x=0

a = -1; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-1)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-1}=\frac{20}{-2}
=-10
$