200+11/2x=54812/5x

Solution for 200+11/2x=54812/5x equation:

200+11/2x=54812/5x

We move all terms to the left:

200+11/2x-(54812/5x)=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-(+54812/5x)+200=0

We get rid of parentheses

11/2x-54812/5x+200=0

We calculate fractions


55x/10x^2+(-109624x)/10x^2+200=0

We multiply all the terms by the denominator


55x+(-109624x)+200*10x^2=0

Wy multiply elements

2000x^2+55x+(-109624x)=0

We get rid of parentheses

2000x^2+55x-109624x=0

We add all the numbers together, and all the variables

2000x^2-109569x=0

a = 2000; b = -109569; c = 0;
Δ = b2-4ac
Δ = -1095692-4·2000·0
Δ = 12005365761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12005365761}=109569$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-109569)-109569}{2*2000}=\frac{0}{4000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109569)+109569}{2*2000}=\frac{219138}{4000}
=54+1569/2000
$