5/3x+x+4x+x+5/3x=300

Solution for 5/3x+x+4x+x+5/3x=300 equation:

5/3x+x+4x+x+5/3x=300

We move all terms to the left:

5/3x+x+4x+x+5/3x-(300)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

6x+5/3x+5/3x-300=0

We multiply all the terms by the denominator


6x*3x-300*3x+5+5=0

We add all the numbers together, and all the variables

6x*3x-300*3x+10=0

Wy multiply elements

18x^2-900x+10=0

a = 18; b = -900; c = +10;
Δ = b2-4ac
Δ = -9002-4·18·10
Δ = 809280
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:

$\sqrt{\Delta}=\sqrt{809280}=\sqrt{576*1405}=\sqrt{576}*\sqrt{1405}=24\sqrt{1405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-24\sqrt{1405}}{2*18}=\frac{900-24\sqrt{1405}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+24\sqrt{1405}}{2*18}=\frac{900+24\sqrt{1405}}{36}
$