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-1/4x+6=2/3x=28
We move all terms to the left:
-1/4x+6-(2/3x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
-1/4x-(+2/3x)+6=0
We get rid of parentheses
-1/4x-2/3x+6=0
We calculate fractions
(-3x)/12x^2+(-8x)/12x^2+6=0
We multiply all the terms by the denominator
(-3x)+(-8x)+6*12x^2=0
Wy multiply elements
72x^2+(-3x)+(-8x)=0
We get rid of parentheses
72x^2-3x-8x=0
We add all the numbers together, and all the variables
72x^2-11x=0
a = 72; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·72·0
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*72}=\frac{0}{144} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*72}=\frac{22}{144} =11/72 $
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