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1/2x+1/3x=6/7
We move all terms to the left:
1/2x+1/3x-(6/7)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
1/2x+1/3x-(+6/7)=0
We get rid of parentheses
1/2x+1/3x-6/7=0
We calculate fractions
(-108x^2)/294x^2+147x/294x^2+98x/294x^2=0
We multiply all the terms by the denominator
(-108x^2)+147x+98x=0
We add all the numbers together, and all the variables
(-108x^2)+245x=0
We get rid of parentheses
-108x^2+245x=0
a = -108; b = 245; c = 0;
Δ = b2-4ac
Δ = 2452-4·(-108)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(245)-245}{2*-108}=\frac{-490}{-216} =2+29/108 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(245)+245}{2*-108}=\frac{0}{-216} =0 $
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