200-11/2x=548-12/5x

Solution for 200-11/2x=548-12/5x equation:

200-11/2x=548-12/5x

We move all terms to the left:

200-11/2x-(548-12/5x)=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+548)+200=0

We get rid of parentheses

-11/2x+12/5x-548+200=0

We calculate fractions


(-55x)/10x^2+24x/10x^2-548+200=0

We add all the numbers together, and all the variables

(-55x)/10x^2+24x/10x^2-348=0

We multiply all the terms by the denominator


(-55x)+24x-348*10x^2=0

We add all the numbers together, and all the variables

24x+(-55x)-348*10x^2=0

Wy multiply elements

-3480x^2+24x+(-55x)=0

We get rid of parentheses

-3480x^2+24x-55x=0

We add all the numbers together, and all the variables

-3480x^2-31x=0

a = -3480; b = -31; c = 0;
Δ = b2-4ac
Δ = -312-4·(-3480)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-31}{2*-3480}=\frac{0}{-6960}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+31}{2*-3480}=\frac{62}{-6960}
=-31/3480
$