200+1(1)/(2)x=546-1(2)/(3)x

Solution for 200+1(1)/(2)x=546-1(2)/(3)x equation:

200+1(1)/(2)x=546-1(2)/(3)x

We move all terms to the left:

200+1(1)/(2)x-(546-1(2)/(3)x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

11/2x-(-12/3x+546)+200=0

We get rid of parentheses

11/2x+12/3x-546+200=0

We calculate fractions


33x/6x^2+24x/6x^2-546+200=0

We add all the numbers together, and all the variables

33x/6x^2+24x/6x^2-346=0

We multiply all the terms by the denominator


33x+24x-346*6x^2=0

We add all the numbers together, and all the variables

57x-346*6x^2=0

Wy multiply elements

-2076x^2+57x=0

a = -2076; b = 57; c = 0;
Δ = b2-4ac
Δ = 572-4·(-2076)·0
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-57}{2*-2076}=\frac{-114}{-4152}
=19/692
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+57}{2*-2076}=\frac{0}{-4152}
=0
$