-8+2/x+4=2x-5-x

Solution for -8+2/x+4=2x-5-x equation:

-8+2/x+4=2x-5-x

We move all terms to the left:

-8+2/x+4-(2x-5-x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2/x-(x-5)-8+4=0

We add all the numbers together, and all the variables

2/x-(x-5)-4=0

We get rid of parentheses

2/x-x+5-4=0

We multiply all the terms by the denominator


-x*x+5*x-4*x+2=0

We add all the numbers together, and all the variables

x-x*x+2=0

Wy multiply elements

-1x^2+x+2=0

a = -1; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-1)·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*-1}=\frac{2}{-2}
=-1
$