x+4/3x=336

Solution for x+4/3x=336 equation:

x+4/3x=336

We move all terms to the left:

x+4/3x-(336)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-336*3x+4=0

Wy multiply elements

3x^2-1008x+4=0

a = 3; b = -1008; c = +4;
Δ = b2-4ac
Δ = -10082-4·3·4
Δ = 1016016
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:

$\sqrt{\Delta}=\sqrt{1016016}=\sqrt{16*63501}=\sqrt{16}*\sqrt{63501}=4\sqrt{63501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1008)-4\sqrt{63501}}{2*3}=\frac{1008-4\sqrt{63501}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1008)+4\sqrt{63501}}{2*3}=\frac{1008+4\sqrt{63501}}{6}
$