8/x+3=x+8/x-4

Solution for 8/x+3=x+8/x-4 equation:

8/x+3=x+8/x-4

We move all terms to the left:

8/x+3-(x+8/x-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

8/x-x-8/x+4+3=0

We multiply all the terms by the denominator


-x*x+4*x+3*x+8-8=0

We add all the numbers together, and all the variables

7x-x*x=0

Wy multiply elements

-1x^2+7x=0

a = -1; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-1)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-1}=\frac{0}{-2}
=0
$