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4/3x+7/6x=1/7
We move all terms to the left:
4/3x+7/6x-(1/7)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x!=0We add all the numbers together, and all the variables
x!=0/6
x!=0
x∈R
4/3x+7/6x-(+1/7)=0
We get rid of parentheses
4/3x+7/6x-1/7=0
We calculate fractions
(-108x^2)/882x^2+1176x/882x^2+1029x/882x^2=0
We multiply all the terms by the denominator
(-108x^2)+1176x+1029x=0
We add all the numbers together, and all the variables
(-108x^2)+2205x=0
We get rid of parentheses
-108x^2+2205x=0
a = -108; b = 2205; c = 0;
Δ = b2-4ac
Δ = 22052-4·(-108)·0
Δ = 4862025
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{4862025}=2205$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2205)-2205}{2*-108}=\frac{-4410}{-216} =20+5/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2205)+2205}{2*-108}=\frac{0}{-216} =0 $
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