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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2+5x=0

a = -2; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-2)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-2}=\frac{0}{-4}
=0
$