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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-4x^2)/4x+2x+(-20x)/4x+5x/4x-1=0

We multiply all the terms by the denominator


(-4x^2)+2x*4x+(-20x)+5x-1*4x=0

We add all the numbers together, and all the variables

(-4x^2)+5x+2x*4x+(-20x)-1*4x=0

Wy multiply elements

(-4x^2)+8x^2+5x+(-20x)-4x=0

We get rid of parentheses

-4x^2+8x^2+5x-20x-4x=0

We add all the numbers together, and all the variables

4x^2-19x=0

a = 4; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·4·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*4}=\frac{38}{8}
=4+3/4
$