1/4x+2=2x

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Solution for 1/4x+2=2x equation:



1/4x+2=2x
We move all terms to the left:
1/4x+2-(2x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We add all the numbers together, and all the variables
-2x+1/4x+2=0
We multiply all the terms by the denominator
-2x*4x+2*4x+1=0
Wy multiply elements
-8x^2+8x+1=0
a = -8; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-8)·1
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*-8}=\frac{-8-4\sqrt{6}}{-16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*-8}=\frac{-8+4\sqrt{6}}{-16} $

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