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1/2x+1=1/4x+4
We move all terms to the left:
1/2x+1-(1/4x+4)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x+4)!=0We get rid of parentheses
x∈R
1/2x-1/4x-4+1=0
We calculate fractions
4x/8x^2+(-2x)/8x^2-4+1=0
We add all the numbers together, and all the variables
4x/8x^2+(-2x)/8x^2-3=0
We multiply all the terms by the denominator
4x+(-2x)-3*8x^2=0
Wy multiply elements
-24x^2+4x+(-2x)=0
We get rid of parentheses
-24x^2+4x-2x=0
We add all the numbers together, and all the variables
-24x^2+2x=0
a = -24; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-24)·0
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-24}=\frac{-4}{-48} =1/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-24}=\frac{0}{-48} =0 $
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