2X-1/x+3=2

Solution for 2X-1/x+3=2 equation:

2X-1/X+3=2

We move all terms to the left:

2X-1/X+3-(2)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

2X-1/X+1=0

We multiply all the terms by the denominator


2X*X+1*X-1=0

We add all the numbers together, and all the variables

X+2X*X-1=0

Wy multiply elements

2X^2+X-1=0

a = 2; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·2·(-1)
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*2}=\frac{-4}{4}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*2}=\frac{2}{4}
=1/2
$