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
$