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

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

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

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-250x^2)/200x^2+20x/200x^2+40x/200x^2=0

We multiply all the terms by the denominator


(-250x^2)+20x+40x=0

We add all the numbers together, and all the variables

(-250x^2)+60x=0

We get rid of parentheses

-250x^2+60x=0

a = -250; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-250)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-250}=\frac{-120}{-500}
=6/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-250}=\frac{0}{-500}
=0
$