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3/4x-2=1/2x-4
We move all terms to the left:
3/4x-2-(1/2x-4)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x-4)!=0We get rid of parentheses
x∈R
3/4x-1/2x+4-2=0
We calculate fractions
6x/8x^2+(-4x)/8x^2+4-2=0
We add all the numbers together, and all the variables
6x/8x^2+(-4x)/8x^2+2=0
We multiply all the terms by the denominator
6x+(-4x)+2*8x^2=0
Wy multiply elements
16x^2+6x+(-4x)=0
We get rid of parentheses
16x^2+6x-4x=0
We add all the numbers together, and all the variables
16x^2+2x=0
a = 16; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·16·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*16}=\frac{-4}{32} =-1/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*16}=\frac{0}{32} =0 $
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