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1/6x+1/3x=3/4
We move all terms to the left:
1/6x+1/3x-(3/4)=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
1/6x+1/3x-(+3/4)=0
We get rid of parentheses
1/6x+1/3x-3/4=0
We calculate fractions
(-162x^2)/288x^2+48x/288x^2+96x/288x^2=0
We multiply all the terms by the denominator
(-162x^2)+48x+96x=0
We add all the numbers together, and all the variables
(-162x^2)+144x=0
We get rid of parentheses
-162x^2+144x=0
a = -162; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-162)·0
Δ = 20736
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{20736}=144$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-162}=\frac{-288}{-324} =8/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-162}=\frac{0}{-324} =0 $
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