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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


4x/3x^2+(-9x)/3x^2-7-4=0

We add all the numbers together, and all the variables

4x/3x^2+(-9x)/3x^2-11=0

We multiply all the terms by the denominator


4x+(-9x)-11*3x^2=0

Wy multiply elements

-33x^2+4x+(-9x)=0

We get rid of parentheses

-33x^2+4x-9x=0

We add all the numbers together, and all the variables

-33x^2-5x=0

a = -33; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-33)·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*-33}=\frac{0}{-66}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-33}=\frac{10}{-66}
=-5/33
$