21-4x=1/2x

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Solution for 21-4x=1/2x equation:



21-4x=1/2x
We move all terms to the left:
21-4x-(1/2x)=0
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
-4x-(+1/2x)+21=0
We get rid of parentheses
-4x-1/2x+21=0
We multiply all the terms by the denominator
-4x*2x+21*2x-1=0
Wy multiply elements
-8x^2+42x-1=0
a = -8; b = 42; c = -1;
Δ = b2-4ac
Δ = 422-4·(-8)·(-1)
Δ = 1732
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:
$\sqrt{\Delta}=\sqrt{1732}=\sqrt{4*433}=\sqrt{4}*\sqrt{433}=2\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{433}}{2*-8}=\frac{-42-2\sqrt{433}}{-16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{433}}{2*-8}=\frac{-42+2\sqrt{433}}{-16} $

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