2/3x=350-x

Solution for 2/3x=350-x equation:

2/3x=350-x

We move all terms to the left:

2/3x-(350-x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-1x+350)=0

We get rid of parentheses

2/3x+1x-350=0

We multiply all the terms by the denominator


1x*3x-350*3x+2=0

Wy multiply elements

3x^2-1050x+2=0

a = 3; b = -1050; c = +2;
Δ = b2-4ac
Δ = -10502-4·3·2
Δ = 1102476
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:

$\sqrt{\Delta}=\sqrt{1102476}=\sqrt{4*275619}=\sqrt{4}*\sqrt{275619}=2\sqrt{275619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1050)-2\sqrt{275619}}{2*3}=\frac{1050-2\sqrt{275619}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1050)+2\sqrt{275619}}{2*3}=\frac{1050+2\sqrt{275619}}{6}
$