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1/3x+1/2x=1/7
We move all terms to the left:
1/3x+1/2x-(1/7)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
1/3x+1/2x-(+1/7)=0
We get rid of parentheses
1/3x+1/2x-1/7=0
We calculate fractions
(-12x^2)/294x^2+98x/294x^2+147x/294x^2=0
We multiply all the terms by the denominator
(-12x^2)+98x+147x=0
We add all the numbers together, and all the variables
(-12x^2)+245x=0
We get rid of parentheses
-12x^2+245x=0
a = -12; b = 245; c = 0;
Δ = b2-4ac
Δ = 2452-4·(-12)·0
Δ = 60025
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{60025}=245$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(245)-245}{2*-12}=\frac{-490}{-24} =20+5/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(245)+245}{2*-12}=\frac{0}{-24} =0 $
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