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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


x+(-10x)/2x+5x/2x-1=0

We multiply all the terms by the denominator


x*2x+(-10x)+5x-1*2x=0

We add all the numbers together, and all the variables

5x+x*2x+(-10x)-1*2x=0

Wy multiply elements

2x^2+5x+(-10x)-2x=0

We get rid of parentheses

2x^2+5x-10x-2x=0

We add all the numbers together, and all the variables

2x^2-7x=0

a = 2; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·2·0
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{-(-7)-7}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*2}=\frac{14}{4}
=3+1/2
$