(1/10)x=3/5

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Solution for (1/10)x=3/5 equation:



(1/10)x=3/5
We move all terms to the left:
(1/10)x-(3/5)=0
Domain of the equation: 10)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+1/10)x-(+3/5)=0
We multiply parentheses
x^2-(+3/5)=0
We get rid of parentheses
x^2-3/5=0
We multiply all the terms by the denominator
x^2*5-3=0
Wy multiply elements
5x^2-3=0
a = 5; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·5·(-3)
Δ = 60
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:
$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*5}=\frac{0-2\sqrt{15}}{10} =-\frac{2\sqrt{15}}{10} =-\frac{\sqrt{15}}{5} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*5}=\frac{0+2\sqrt{15}}{10} =\frac{2\sqrt{15}}{10} =\frac{\sqrt{15}}{5} $

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