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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+2)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


20x/50x^2+(-15x)/50x^2-2-1=0

We add all the numbers together, and all the variables

20x/50x^2+(-15x)/50x^2-3=0

We multiply all the terms by the denominator


20x+(-15x)-3*50x^2=0

Wy multiply elements

-150x^2+20x+(-15x)=0

We get rid of parentheses

-150x^2+20x-15x=0

We add all the numbers together, and all the variables

-150x^2+5x=0

a = -150; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-150)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-150}=\frac{-10}{-300}
=1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-150}=\frac{0}{-300}
=0
$