5x/3x-9/x=4

Solution for 5x/3x-9/x=4 equation:

5x/3x-9/x=4

We move all terms to the left:

5x/3x-9/x-(4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


5x^2/3x^2+(-27x)/3x^2-4=0

We multiply all the terms by the denominator


5x^2+(-27x)-4*3x^2=0

Wy multiply elements

5x^2-12x^2+(-27x)=0

We get rid of parentheses

5x^2-12x^2-27x=0

We add all the numbers together, and all the variables

-7x^2-27x=0

a = -7; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-7)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-7}=\frac{0}{-14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-7}=\frac{54}{-14}
=-3+6/7
$