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3/x+2/7x=10/9
We move all terms to the left:
3/x+2/7x-(10/9)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 7x!=0We add all the numbers together, and all the variables
x!=0/7
x!=0
x∈R
3/x+2/7x-(+10/9)=0
We get rid of parentheses
3/x+2/7x-10/9=0
We calculate fractions
(-490x^2)/567x^2+1701x/567x^2+162x/567x^2=0
We multiply all the terms by the denominator
(-490x^2)+1701x+162x=0
We add all the numbers together, and all the variables
(-490x^2)+1863x=0
We get rid of parentheses
-490x^2+1863x=0
a = -490; b = 1863; c = 0;
Δ = b2-4ac
Δ = 18632-4·(-490)·0
Δ = 3470769
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{3470769}=1863$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1863)-1863}{2*-490}=\frac{-3726}{-980} =3+393/490 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1863)+1863}{2*-490}=\frac{0}{-980} =0 $
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