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4/7-2/3x=8/12x
We move all terms to the left:
4/7-2/3x-(8/12x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 12x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
-2/3x-(+8/12x)+4/7=0
We get rid of parentheses
-2/3x-8/12x+4/7=0
We calculate fractions
144x^2/1764x^2+(-1176x)/1764x^2+(-1176x)/1764x^2=0
We multiply all the terms by the denominator
144x^2+(-1176x)+(-1176x)=0
We get rid of parentheses
144x^2-1176x-1176x=0
We add all the numbers together, and all the variables
144x^2-2352x=0
a = 144; b = -2352; c = 0;
Δ = b2-4ac
Δ = -23522-4·144·0
Δ = 5531904
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{5531904}=2352$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2352)-2352}{2*144}=\frac{0}{288} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2352)+2352}{2*144}=\frac{4704}{288} =16+1/3 $
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