X+2/3x+x+2/3x=400

Solution for X+2/3x+x+2/3x=400 equation:

X+2/3X+X+2/3X=400

We move all terms to the left:

X+2/3X+X+2/3X-(400)=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+2/3X+2/3X-400=0

We multiply all the terms by the denominator


2X*3X-400*3X+2+2=0

We add all the numbers together, and all the variables

2X*3X-400*3X+4=0

Wy multiply elements

6X^2-1200X+4=0

a = 6; b = -1200; c = +4;
Δ = b2-4ac
Δ = -12002-4·6·4
Δ = 1439904
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:

$\sqrt{\Delta}=\sqrt{1439904}=\sqrt{16*89994}=\sqrt{16}*\sqrt{89994}=4\sqrt{89994}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-4\sqrt{89994}}{2*6}=\frac{1200-4\sqrt{89994}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+4\sqrt{89994}}{2*6}=\frac{1200+4\sqrt{89994}}{12}
$