1/2x-5=3/10x

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

1/2x-5=3/10x

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


10x/20x^2+(-6x)/20x^2-5=0

We multiply all the terms by the denominator


10x+(-6x)-5*20x^2=0

Wy multiply elements

-100x^2+10x+(-6x)=0

We get rid of parentheses

-100x^2+10x-6x=0

We add all the numbers together, and all the variables

-100x^2+4x=0

a = -100; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-100)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-100}=\frac{-8}{-200}
=1/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-100}=\frac{0}{-200}
=0
$