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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)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
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 $
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