3/x-4=5/2x-7

Solution for 3/x-4=5/2x-7 equation:

3/x-4=5/2x-7

We move all terms to the left:

3/x-4-(5/2x-7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

3/x-5/2x+7-4=0

We calculate fractions


6x/2x^2+(-5x)/2x^2+7-4=0

We add all the numbers together, and all the variables

6x/2x^2+(-5x)/2x^2+3=0

We multiply all the terms by the denominator


6x+(-5x)+3*2x^2=0

Wy multiply elements

6x^2+6x+(-5x)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+x=0

a = 6; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·6·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*6}=\frac{-2}{12}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*6}=\frac{0}{12}
=0
$