(1)/(2)x-16=-28-(1)/(4)x

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Solution for (1)/(2)x-16=-28-(1)/(4)x equation:



(1)/(2)x-16=-28-(1)/(4)x
We move all terms to the left:
(1)/(2)x-16-(-28-(1)/(4)x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/2x-(-1/4x-28)-16=0
We get rid of parentheses
1/2x+1/4x+28-16=0
We calculate fractions
4x/8x^2+2x/8x^2+28-16=0
We add all the numbers together, and all the variables
4x/8x^2+2x/8x^2+12=0
We multiply all the terms by the denominator
4x+2x+12*8x^2=0
We add all the numbers together, and all the variables
6x+12*8x^2=0
Wy multiply elements
96x^2+6x=0
a = 96; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·96·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*96}=\frac{-12}{192} =-1/16 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*96}=\frac{0}{192} =0 $

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