2/3*x+x=300

Solution for 2/3*x+x=300 equation:

2/3x+x=300

We move all terms to the left:

2/3x+x-(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

x+2/3x-300=0

We multiply all the terms by the denominator


x*3x-300*3x+2=0

Wy multiply elements

3x^2-900x+2=0

a = 3; b = -900; c = +2;
Δ = b2-4ac
Δ = -9002-4·3·2
Δ = 809976
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:

$\sqrt{\Delta}=\sqrt{809976}=\sqrt{4*202494}=\sqrt{4}*\sqrt{202494}=2\sqrt{202494}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-2\sqrt{202494}}{2*3}=\frac{900-2\sqrt{202494}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+2\sqrt{202494}}{2*3}=\frac{900+2\sqrt{202494}}{6}
$