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61/9x+3/13x=281/3
We move all terms to the left:
61/9x+3/13x-(281/3)=0
Domain of the equation: 9x!=0
x!=0/9
x!=0
x∈R
Domain of the equation: 13x!=0We add all the numbers together, and all the variables
x!=0/13
x!=0
x∈R
61/9x+3/13x-(+281/3)=0
We get rid of parentheses
61/9x+3/13x-281/3=0
We calculate fractions
(-32877x^2)/1053x^2+7137x/1053x^2+243x/1053x^2=0
We multiply all the terms by the denominator
(-32877x^2)+7137x+243x=0
We add all the numbers together, and all the variables
(-32877x^2)+7380x=0
We get rid of parentheses
-32877x^2+7380x=0
a = -32877; b = 7380; c = 0;
Δ = b2-4ac
Δ = 73802-4·(-32877)·0
Δ = 54464400
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{54464400}=7380$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7380)-7380}{2*-32877}=\frac{-14760}{-65754} =820/3653 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7380)+7380}{2*-32877}=\frac{0}{-65754} =0 $
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