5/x-1-7/x=3/2x-2

Solution for 5/x-1-7/x=3/2x-2 equation:

5/x-1-7/x=3/2x-2

We move all terms to the left:

5/x-1-7/x-(3/2x-2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-2)!=0

x∈R


We get rid of parentheses

5/x-7/x-3/2x+2-1=0

We calculate fractions


(-14x+5)/2x^2+(-3x)/2x^2+2-1=0

We add all the numbers together, and all the variables

(-14x+5)/2x^2+(-3x)/2x^2+1=0

We multiply all the terms by the denominator


(-14x+5)+(-3x)+1*2x^2=0

Wy multiply elements

2x^2+(-14x+5)+(-3x)=0

We get rid of parentheses

2x^2-14x-3x+5=0

We add all the numbers together, and all the variables

2x^2-17x+5=0

a = 2; b = -17; c = +5;
Δ = b2-4ac
Δ = -172-4·2·5
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{249}}{2*2}=\frac{17-\sqrt{249}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{249}}{2*2}=\frac{17+\sqrt{249}}{4}
$