1/2x-3/5=3/10x-4

Solution for 1/2x-3/5=3/10x-4 equation:

1/2x-3/5=3/10x-4

We move all terms to the left:

1/2x-3/5-(3/10x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x-4)!=0

x∈R


We get rid of parentheses

1/2x-3/10x+4-3/5=0

We calculate fractions


(-60x^2)/500x^2+250x/500x^2+(-150x)/500x^2+4=0

We multiply all the terms by the denominator


(-60x^2)+250x+(-150x)+4*500x^2=0

Wy multiply elements

(-60x^2)+2000x^2+250x+(-150x)=0

We get rid of parentheses

-60x^2+2000x^2+250x-150x=0

We add all the numbers together, and all the variables

1940x^2+100x=0

a = 1940; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·1940·0
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*1940}=\frac{-200}{3880}
=-5/97
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*1940}=\frac{0}{3880}
=0
$