X2+8x=-x

Solution for X2+8x=-x equation:

X2+8X=-X

We move all terms to the left:

X2+8X-(-X)=0

We add all the numbers together, and all the variables

X2+8X-(-1X)=0

We add all the numbers together, and all the variables

X^2+8X-(-1X)=0

We get rid of parentheses

X^2+8X+1X=0

We add all the numbers together, and all the variables

X^2+9X=0

a = 1; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·1·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*1}=\frac{-18}{2}
=-9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*1}=\frac{0}{2}
=0
$