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

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

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

We move all terms to the left:

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


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


40x^2/500x^2+150x/500x^2+(-750x)/500x^2=0

We multiply all the terms by the denominator


40x^2+150x+(-750x)=0

We get rid of parentheses

40x^2+150x-750x=0

We add all the numbers together, and all the variables

40x^2-600x=0

a = 40; b = -600; c = 0;
Δ = b2-4ac
Δ = -6002-4·40·0
Δ = 360000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{360000}=600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-600}{2*40}=\frac{0}{80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+600}{2*40}=\frac{1200}{80}
=15
$