6/x-(1/4)=8/2xx=

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Solution for 6/x-(1/4)=8/2xx= equation:



6/x-(1/4)=8/2xx=
We move all terms to the left:
6/x-(1/4)-(8/2xx)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2xx)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
6/x-(+8/2xx)-(+1/4)=0
We get rid of parentheses
6/x-8/2xx-1/4=0
We calculate fractions
(-4x^2)/32x^2+192x/32x^2+(-128x)/32x^2=0
We multiply all the terms by the denominator
(-4x^2)+192x+(-128x)=0
We get rid of parentheses
-4x^2+192x-128x=0
We add all the numbers together, and all the variables
-4x^2+64x=0
a = -4; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-4)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*-4}=\frac{-128}{-8} =+16 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-4}=\frac{0}{-8} =0 $

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