1/x-1=7/2x+5

Solution for 1/x-1=7/2x+5 equation:

1/x-1=7/2x+5

We move all terms to the left:

1/x-1-(7/2x+5)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

1/x-7/2x-5-1=0

We calculate fractions


2x/2x^2+(-7x)/2x^2-5-1=0

We add all the numbers together, and all the variables

2x/2x^2+(-7x)/2x^2-6=0

We multiply all the terms by the denominator


2x+(-7x)-6*2x^2=0

Wy multiply elements

-12x^2+2x+(-7x)=0

We get rid of parentheses

-12x^2+2x-7x=0

We add all the numbers together, and all the variables

-12x^2-5x=0

a = -12; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-12)·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*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-12}=\frac{10}{-24}
=-5/12
$