4/3X=7-3/x

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

4/3X=7-3/X

We move all terms to the left:

4/3X-(7-3/X)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R



Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/3X+3/X-7=0

We calculate fractions


4X/3X^2+9X/3X^2-7=0

We multiply all the terms by the denominator


4X+9X-7*3X^2=0

We add all the numbers together, and all the variables

13X-7*3X^2=0

Wy multiply elements

-21X^2+13X=0

a = -21; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-21)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-21}=\frac{-26}{-42}
=13/21
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-21}=\frac{0}{-42}
=0
$