1/2x+3=1/10x

Solution for 1/2x+3=1/10x equation:

1/2x+3=1/10x

We move all terms to the left:

1/2x+3-(1/10x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+1/10x)+3=0

We get rid of parentheses

1/2x-1/10x+3=0

We calculate fractions


10x/20x^2+(-2x)/20x^2+3=0

We multiply all the terms by the denominator


10x+(-2x)+3*20x^2=0

Wy multiply elements

60x^2+10x+(-2x)=0

We get rid of parentheses

60x^2+10x-2x=0

We add all the numbers together, and all the variables

60x^2+8x=0

a = 60; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·60·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*60}=\frac{-16}{120}
=-2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*60}=\frac{0}{120}
=0
$