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2/7x+5/21x=142/3
We move all terms to the left:
2/7x+5/21x-(142/3)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 21x!=0We add all the numbers together, and all the variables
x!=0/21
x!=0
x∈R
2/7x+5/21x-(+142/3)=0
We get rid of parentheses
2/7x+5/21x-142/3=0
We calculate fractions
(-41748x^2)/1323x^2+378x/1323x^2+315x/1323x^2=0
We multiply all the terms by the denominator
(-41748x^2)+378x+315x=0
We add all the numbers together, and all the variables
(-41748x^2)+693x=0
We get rid of parentheses
-41748x^2+693x=0
a = -41748; b = 693; c = 0;
Δ = b2-4ac
Δ = 6932-4·(-41748)·0
Δ = 480249
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{480249}=693$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(693)-693}{2*-41748}=\frac{-1386}{-83496} =33/1988 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(693)+693}{2*-41748}=\frac{0}{-83496} =0 $
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