(4/3x)+4x=18

Solution for (4/3x)+4x=18 equation:

(4/3x)+4x=18

We move all terms to the left:

(4/3x)+4x-(18)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/3x)+4x-18=0

We add all the numbers together, and all the variables

4x+(+4/3x)-18=0

We get rid of parentheses

4x+4/3x-18=0

We multiply all the terms by the denominator


4x*3x-18*3x+4=0

Wy multiply elements

12x^2-54x+4=0

a = 12; b = -54; c = +4;
Δ = b2-4ac
Δ = -542-4·12·4
Δ = 2724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2724}=\sqrt{4*681}=\sqrt{4}*\sqrt{681}=2\sqrt{681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{681}}{2*12}=\frac{54-2\sqrt{681}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{681}}{2*12}=\frac{54+2\sqrt{681}}{24}
$