200+11/2x=584-12/5x

Solution for 200+11/2x=584-12/5x equation:

200+11/2x=584-12/5x

We move all terms to the left:

200+11/2x-(584-12/5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

11/2x-(-12/5x+584)+200=0

We get rid of parentheses

11/2x+12/5x-584+200=0

We calculate fractions


55x/10x^2+24x/10x^2-584+200=0

We add all the numbers together, and all the variables

55x/10x^2+24x/10x^2-384=0

We multiply all the terms by the denominator


55x+24x-384*10x^2=0

We add all the numbers together, and all the variables

79x-384*10x^2=0

Wy multiply elements

-3840x^2+79x=0

a = -3840; b = 79; c = 0;
Δ = b2-4ac
Δ = 792-4·(-3840)·0
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(79)-79}{2*-3840}=\frac{-158}{-7680}
=79/3840
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(79)+79}{2*-3840}=\frac{0}{-7680}
=0
$