5(20x+10)=5/10x

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Solution for 5(20x+10)=5/10x equation:



5(20x+10)=5/10x
We move all terms to the left:
5(20x+10)-(5/10x)=0
Domain of the equation: 10x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
5(20x+10)-(+5/10x)=0
We multiply parentheses
100x-(+5/10x)+50=0
We get rid of parentheses
100x-5/10x+50=0
We multiply all the terms by the denominator
100x*10x+50*10x-5=0
Wy multiply elements
1000x^2+500x-5=0
a = 1000; b = 500; c = -5;
Δ = b2-4ac
Δ = 5002-4·1000·(-5)
Δ = 270000
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:
$\sqrt{\Delta}=\sqrt{270000}=\sqrt{90000*3}=\sqrt{90000}*\sqrt{3}=300\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-300\sqrt{3}}{2*1000}=\frac{-500-300\sqrt{3}}{2000} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+300\sqrt{3}}{2*1000}=\frac{-500+300\sqrt{3}}{2000} $

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