x/x-3=2x-5/2x+1

Solution for x/x-3=2x-5/2x+1 equation:

x/x-3=2x-5/2x+1

We move all terms to the left:

x/x-3-(2x-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

x/x-2x+5/2x-1-3=0

Fractions to decimals

5/2x-2x-1-3+1=0

We multiply all the terms by the denominator


-2x*2x-1*2x-3*2x+1*2x+5=0

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -4; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·(-4)·5
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{29}}{2*-4}=\frac{6-2\sqrt{29}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{29}}{2*-4}=\frac{6+2\sqrt{29}}{-8}
$