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

Solution for 2x+1/x-1+4=0 equation:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/x+3=0

We multiply all the terms by the denominator


2x*x+3*x+1=0

We add all the numbers together, and all the variables

3x+2x*x+1=0

Wy multiply elements

2x^2+3x+1=0

a = 2; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·2·1
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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