20+3x=1/2x

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Solution for 20+3x=1/2x equation:



20+3x=1/2x
We move all terms to the left:
20+3x-(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
3x-(+1/2x)+20=0
We get rid of parentheses
3x-1/2x+20=0
We multiply all the terms by the denominator
3x*2x+20*2x-1=0
Wy multiply elements
6x^2+40x-1=0
a = 6; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·6·(-1)
Δ = 1624
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:
$\sqrt{\Delta}=\sqrt{1624}=\sqrt{4*406}=\sqrt{4}*\sqrt{406}=2\sqrt{406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{406}}{2*6}=\frac{-40-2\sqrt{406}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{406}}{2*6}=\frac{-40+2\sqrt{406}}{12} $

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