x+8/x+4=2x+1/x+8

Solution for x+8/x+4=2x+1/x+8 equation:

x+8/x+4=2x+1/x+8

We move all terms to the left:

x+8/x+4-(2x+1/x+8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+8)!=0

x∈R


We get rid of parentheses

x+8/x-2x-1/x-8+4=0

We multiply all the terms by the denominator


x*x-2x*x-8*x+4*x+8-1=0

We add all the numbers together, and all the variables

-4x+x*x-2x*x+7=0

Wy multiply elements

x^2-2x^2-4x+7=0

We add all the numbers together, and all the variables

-1x^2-4x+7=0

a = -1; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-1)·7
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{11}}{2*-1}=\frac{4-2\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{11}}{2*-1}=\frac{4+2\sqrt{11}}{-2}
$