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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

2/x-5/2x+1+2=0

We calculate fractions


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

We add all the numbers together, and all the variables

4x/2x^2+(-5x)/2x^2+3=0

We multiply all the terms by the denominator


4x+(-5x)+3*2x^2=0

Wy multiply elements

6x^2+4x+(-5x)=0

We get rid of parentheses

6x^2+4x-5x=0

We add all the numbers together, and all the variables

6x^2-1x=0

a = 6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·6·0
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{-(-1)-1}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*6}=\frac{2}{12}
=1/6
$