(4x/9)-8=(108/4x)

Solution for (4x/9)-8=(108/4x) equation:

(4x/9)-8=(108/4x)

We move all terms to the left:

(4x/9)-8-((108/4x))=0


Domain of the equation: 4x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4x/9)-((+108/4x))-8=0

We get rid of parentheses

4x/9-((+108/4x))-8=0

We calculate fractions


16x^2/36x+()/36x-8=0

We multiply all the terms by the denominator


16x^2-8*36x+()=0

We add all the numbers together, and all the variables

16x^2-8*36x=0

Wy multiply elements

16x^2-288x=0

a = 16; b = -288; c = 0;
Δ = b2-4ac
Δ = -2882-4·16·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-288}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+288}{2*16}=\frac{576}{32}
=18
$