8/3x-9-5/x-3=4

Solution for 8/3x-9-5/x-3=4 equation:

8/3x-9-5/x-3=4

We move all terms to the left:

8/3x-9-5/x-3-(4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

8/3x-5/x-16=0

We calculate fractions


8x/3x^2+(-15x)/3x^2-16=0

We multiply all the terms by the denominator


8x+(-15x)-16*3x^2=0

Wy multiply elements

-48x^2+8x+(-15x)=0

We get rid of parentheses

-48x^2+8x-15x=0

We add all the numbers together, and all the variables

-48x^2-7x=0

a = -48; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-48)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-48}=\frac{14}{-96}
=-7/48
$