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

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
$