2x/x-4+2x-5/x-3=25/3

Solution for 2x/x-4+2x-5/x-3=25/3 equation:

2x/x-4+2x-5/x-3=25/3

We move all terms to the left:

2x/x-4+2x-5/x-3-(25/3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x/x+2x-5/x-4-3-(+25/3)=0

We add all the numbers together, and all the variables

2x+2x/x-5/x-7-(+25/3)=0

We get rid of parentheses

2x+2x/x-5/x-7-25/3=0

We calculate fractions


2x+(2x-15)/3x+(-25x)/3x-7=0

We multiply all the terms by the denominator


2x*3x+(2x-15)+(-25x)-7*3x=0

Wy multiply elements

6x^2+(2x-15)+(-25x)-21x=0

We get rid of parentheses

6x^2+2x-25x-21x-15=0

We add all the numbers together, and all the variables

6x^2-44x-15=0

a = 6; b = -44; c = -15;
Δ = b2-4ac
Δ = -442-4·6·(-15)
Δ = 2296
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:

$\sqrt{\Delta}=\sqrt{2296}=\sqrt{4*574}=\sqrt{4}*\sqrt{574}=2\sqrt{574}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{574}}{2*6}=\frac{44-2\sqrt{574}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{574}}{2*6}=\frac{44+2\sqrt{574}}{12}
$