3/x-2=7/4x-8

Solution for 3/x-2=7/4x-8 equation:

3/x-2=7/4x-8

We move all terms to the left:

3/x-2-(7/4x-8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x-8)!=0

x∈R


We get rid of parentheses

3/x-7/4x+8-2=0

We calculate fractions


12x/4x^2+(-7x)/4x^2+8-2=0

We add all the numbers together, and all the variables

12x/4x^2+(-7x)/4x^2+6=0

We multiply all the terms by the denominator


12x+(-7x)+6*4x^2=0

Wy multiply elements

24x^2+12x+(-7x)=0

We get rid of parentheses

24x^2+12x-7x=0

We add all the numbers together, and all the variables

24x^2+5x=0

a = 24; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·24·0
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*24}=\frac{-10}{48}
=-5/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*24}=\frac{0}{48}
=0
$