(13+x)(13-x)=-x

Solution for (13+x)(13-x)=-x equation:

(13+x)(13-x)=-x

We move all terms to the left:

(13+x)(13-x)-(-x)=0

We add all the numbers together, and all the variables

(x+13)(-1x+13)-(-1x)=0

We get rid of parentheses

(x+13)(-1x+13)+1x=0

We multiply parentheses ..

(-1x^2+13x-13x+169)+1x=0

We add all the numbers together, and all the variables

(-1x^2+13x-13x+169)+x=0

We get rid of parentheses

-1x^2+13x-13x+x+169=0

We add all the numbers together, and all the variables

-1x^2+x+169=0

a = -1; b = 1; c = +169;
Δ = b2-4ac
Δ = 12-4·(-1)·169
Δ = 677
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{-(1)-\sqrt{677}}{2*-1}=\frac{-1-\sqrt{677}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{677}}{2*-1}=\frac{-1+\sqrt{677}}{-2}
$