4x-(1/8)x=2

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



4x-(1/8)x=2
We move all terms to the left:
4x-(1/8)x-(2)=0
Domain of the equation: 8)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
4x-(+1/8)x-2=0
We multiply parentheses
-x^2+4x-2=0
We add all the numbers together, and all the variables
-1x^2+4x-2=0
a = -1; b = 4; c = -2;
Δ = b2-4ac
Δ = 42-4·(-1)·(-2)
Δ = 8
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:
$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{2}}{2*-1}=\frac{-4-2\sqrt{2}}{-2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{2}}{2*-1}=\frac{-4+2\sqrt{2}}{-2} $

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