3/2x-1=4/x+7

Solution for 3/2x-1=4/x+7 equation:

3/2x-1=4/x+7

We move all terms to the left:

3/2x-1-(4/x+7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+7)!=0

x∈R


We get rid of parentheses

3/2x-4/x-7-1=0

We calculate fractions


3x/2x^2+(-8x)/2x^2-7-1=0

We add all the numbers together, and all the variables

3x/2x^2+(-8x)/2x^2-8=0

We multiply all the terms by the denominator


3x+(-8x)-8*2x^2=0

Wy multiply elements

-16x^2+3x+(-8x)=0

We get rid of parentheses

-16x^2+3x-8x=0

We add all the numbers together, and all the variables

-16x^2-5x=0

a = -16; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-16)·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*-16}=\frac{0}{-32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-16}=\frac{10}{-32}
=-5/16
$