3/4x-4+7=1/2x

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Solution for 3/4x-4+7=1/2x equation:



3/4x-4+7=1/2x
We move all terms to the left:
3/4x-4+7-(1/2x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
3/4x-(+1/2x)-4+7=0
We add all the numbers together, and all the variables
3/4x-(+1/2x)+3=0
We get rid of parentheses
3/4x-1/2x+3=0
We calculate fractions
6x/8x^2+(-4x)/8x^2+3=0
We multiply all the terms by the denominator
6x+(-4x)+3*8x^2=0
Wy multiply elements
24x^2+6x+(-4x)=0
We get rid of parentheses
24x^2+6x-4x=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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