2x-1/x-4/x+2=5

Solution for 2x-1/x-4/x+2=5 equation:

2x-1/x-4/x+2=5

We move all terms to the left:

2x-1/x-4/x+2-(5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-1/x-4/x-3=0

We multiply all the terms by the denominator


2x*x-3*x-1-4=0

We add all the numbers together, and all the variables

-3x+2x*x-5=0

Wy multiply elements

2x^2-3x-5=0

a = 2; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·2·(-5)
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{-(-3)-7}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*2}=\frac{10}{4}
=2+1/2
$