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12x(1/4)+12x(1/6)+12x(1/2)=x
We move all terms to the left:
12x(1/4)+12x(1/6)+12x(1/2)-(x)=0
We add all the numbers together, and all the variables
12x(+1/4)+12x(+1/6)+12x(+1/2)-x=0
We add all the numbers together, and all the variables
-1x+12x(+1/4)+12x(+1/6)+12x(+1/2)=0
We multiply parentheses
12x^2+12x^2+12x^2-1x=0
We add all the numbers together, and all the variables
36x^2-1x=0
a = 36; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·36·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*36}=\frac{0}{72} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*36}=\frac{2}{72} =1/36 $
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