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3/4x+3/4-1/2x=-1
We move all terms to the left:
3/4x+3/4-1/2x-(-1)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
3/4x-1/2x+1+3/4=0
We calculate fractions
6x/128x^2+(-64x)/128x^2+6x/128x^2+1=0
We multiply all the terms by the denominator
6x+(-64x)+6x+1*128x^2=0
We add all the numbers together, and all the variables
12x+(-64x)+1*128x^2=0
Wy multiply elements
128x^2+12x+(-64x)=0
We get rid of parentheses
128x^2+12x-64x=0
We add all the numbers together, and all the variables
128x^2-52x=0
a = 128; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·128·0
Δ = 2704
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{2704}=52$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*128}=\frac{0}{256} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*128}=\frac{104}{256} =13/32 $
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