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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-50x^2)/200x^2+120x/200x^2+(-20x)/200x^2-1=0

We multiply all the terms by the denominator


(-50x^2)+120x+(-20x)-1*200x^2=0

Wy multiply elements

(-50x^2)-200x^2+120x+(-20x)=0

We get rid of parentheses

-50x^2-200x^2+120x-20x=0

We add all the numbers together, and all the variables

-250x^2+100x=0

a = -250; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·(-250)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*-250}=\frac{-200}{-500}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*-250}=\frac{0}{-500}
=0
$