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

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

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

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


15x/50x^2+20x/50x^2-4+1=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

35x-3*50x^2=0

Wy multiply elements

-150x^2+35x=0

a = -150; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-150)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-150}=\frac{-70}{-300}
=7/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-150}=\frac{0}{-300}
=0
$