200+1(1)/(2)x=548+1(2)/(5)x

Solution for 200+1(1)/(2)x=548+1(2)/(5)x equation:

200+1(1)/(2)x=548+1(2)/(5)x

We move all terms to the left:

200+1(1)/(2)x-(548+1(2)/(5)x)=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

Wy multiply elements

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

We get rid of parentheses

-3480x^2+55x-24x=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{-62}{-6960}
=31/3480
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-3480}=\frac{0}{-6960}
=0
$