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5/6x-2/3x=3/8
We move all terms to the left:
5/6x-2/3x-(3/8)=0
Domain of the equation: 6x!=0
x!=0/6
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
5/6x-2/3x-(+3/8)=0
We get rid of parentheses
5/6x-2/3x-3/8=0
We calculate fractions
(-162x^2)/1152x^2+960x/1152x^2+(-768x)/1152x^2=0
We multiply all the terms by the denominator
(-162x^2)+960x+(-768x)=0
We get rid of parentheses
-162x^2+960x-768x=0
We add all the numbers together, and all the variables
-162x^2+192x=0
a = -162; b = 192; c = 0;
Δ = b2-4ac
Δ = 1922-4·(-162)·0
Δ = 36864
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{36864}=192$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-192}{2*-162}=\frac{-384}{-324} =1+5/27 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+192}{2*-162}=\frac{0}{-324} =0 $
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