x+4/3x=192

Solution for x+4/3x=192 equation:

x+4/3x=192

We move all terms to the left:

x+4/3x-(192)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-192*3x+4=0

Wy multiply elements

3x^2-576x+4=0

a = 3; b = -576; c = +4;
Δ = b2-4ac
Δ = -5762-4·3·4
Δ = 331728
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:

$\sqrt{\Delta}=\sqrt{331728}=\sqrt{16*20733}=\sqrt{16}*\sqrt{20733}=4\sqrt{20733}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-576)-4\sqrt{20733}}{2*3}=\frac{576-4\sqrt{20733}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-576)+4\sqrt{20733}}{2*3}=\frac{576+4\sqrt{20733}}{6}
$