5x-10=1/2x

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Solution for 5x-10=1/2x equation:



5x-10=1/2x
We move all terms to the left:
5x-10-(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
5x-(+1/2x)-10=0
We get rid of parentheses
5x-1/2x-10=0
We multiply all the terms by the denominator
5x*2x-10*2x-1=0
Wy multiply elements
10x^2-20x-1=0
a = 10; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·10·(-1)
Δ = 440
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:
$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{110}}{2*10}=\frac{20-2\sqrt{110}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{110}}{2*10}=\frac{20+2\sqrt{110}}{20} $

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