x+13/x=-8

Solution for x+13/x=-8 equation:

x+13/x=-8

We move all terms to the left:

x+13/x-(-8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+13/x+8=0

We multiply all the terms by the denominator


x*x+8*x+13=0

We add all the numbers together, and all the variables

8x+x*x+13=0

Wy multiply elements

x^2+8x+13=0

a = 1; b = 8; c = +13;
Δ = b2-4ac
Δ = 82-4·1·13
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{3}}{2*1}=\frac{-8-2\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{3}}{2*1}=\frac{-8+2\sqrt{3}}{2}
$