x-4/x+8=-2

Solution for x-4/x+8=-2 equation:

x-4/x+8=-2

We move all terms to the left:

x-4/x+8-(-2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-4/x+10=0

We multiply all the terms by the denominator


x*x+10*x-4=0

We add all the numbers together, and all the variables

10x+x*x-4=0

Wy multiply elements

x^2+10x-4=0

a = 1; b = 10; c = -4;
Δ = b2-4ac
Δ = 102-4·1·(-4)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{29}}{2*1}=\frac{-10-2\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{29}}{2*1}=\frac{-10+2\sqrt{29}}{2}
$