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

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

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

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


120x^2/500x^2+(-50x)/500x^2+(-250x)/500x^2-1=0

We multiply all the terms by the denominator


120x^2+(-50x)+(-250x)-1*500x^2=0

Wy multiply elements

120x^2-500x^2+(-50x)+(-250x)=0

We get rid of parentheses

120x^2-500x^2-50x-250x=0

We add all the numbers together, and all the variables

-380x^2-300x=0

a = -380; b = -300; c = 0;
Δ = b2-4ac
Δ = -3002-4·(-380)·0
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-300}{2*-380}=\frac{0}{-760}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+300}{2*-380}=\frac{600}{-760}
=-15/19
$