1/2x+16=4+-2/3x

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Solution for 1/2x+16=4+-2/3x equation:



1/2x+16=4+-2/3x
We move all terms to the left:
1/2x+16-(4+-2/3x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/2x-(-2/3x)+16=0
We get rid of parentheses
1/2x+2/3x+16=0
We calculate fractions
3x/6x^2+4x/6x^2+16=0
We multiply all the terms by the denominator
3x+4x+16*6x^2=0
We add all the numbers together, and all the variables
7x+16*6x^2=0
Wy multiply elements
96x^2+7x=0
a = 96; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·96·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*96}=\frac{-14}{192} =-7/96 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*96}=\frac{0}{192} =0 $

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