4/3x+2x=60

Solution for 4/3x+2x=60 equation:

4/3x+2x=60

We move all terms to the left:

4/3x+2x-(60)=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-60=0

We multiply all the terms by the denominator


2x*3x-60*3x+4=0

Wy multiply elements

6x^2-180x+4=0

a = 6; b = -180; c = +4;
Δ = b2-4ac
Δ = -1802-4·6·4
Δ = 32304
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:

$\sqrt{\Delta}=\sqrt{32304}=\sqrt{16*2019}=\sqrt{16}*\sqrt{2019}=4\sqrt{2019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-4\sqrt{2019}}{2*6}=\frac{180-4\sqrt{2019}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+4\sqrt{2019}}{2*6}=\frac{180+4\sqrt{2019}}{12}
$