120+4/3x=2x

Solution for 120+4/3x=2x equation:

120+4/3x=2x

We move all terms to the left:

120+4/3x-(2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+4/3x+120=0

We multiply all the terms by the denominator


-2x*3x+120*3x+4=0

Wy multiply elements

-6x^2+360x+4=0

a = -6; b = 360; c = +4;
Δ = b2-4ac
Δ = 3602-4·(-6)·4
Δ = 129696
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:

$\sqrt{\Delta}=\sqrt{129696}=\sqrt{16*8106}=\sqrt{16}*\sqrt{8106}=4\sqrt{8106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-4\sqrt{8106}}{2*-6}=\frac{-360-4\sqrt{8106}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+4\sqrt{8106}}{2*-6}=\frac{-360+4\sqrt{8106}}{-12}
$