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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 10x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


60x^2/750x^2+250x/750x^2+(-225x)/750x^2+1=0

We multiply all the terms by the denominator


60x^2+250x+(-225x)+1*750x^2=0

Wy multiply elements

60x^2+750x^2+250x+(-225x)=0

We get rid of parentheses

60x^2+750x^2+250x-225x=0

We add all the numbers together, and all the variables

810x^2+25x=0

a = 810; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·810·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*810}=\frac{-50}{1620}
=-5/162
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*810}=\frac{0}{1620}
=0
$