3/10+1/5x=1/2x

Solution for 3/10+1/5x=1/2x equation:

3/10+1/5x=1/2x

We move all terms to the left:

3/10+1/5x-(1/2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(+1/2x)+3/10=0

We get rid of parentheses

1/5x-1/2x+3/10=0

We calculate fractions


60x^2/100x^2+20x/100x^2+(-50x)/100x^2=0

We multiply all the terms by the denominator


60x^2+20x+(-50x)=0

We get rid of parentheses

60x^2+20x-50x=0

We add all the numbers together, and all the variables

60x^2-30x=0

a = 60; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·60·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*60}=\frac{0}{120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*60}=\frac{60}{120}
=1/2
$