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

Solution for 4/(5*x)+1/10=3/(2*x) equation:

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

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

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

We get rid of parentheses

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

We calculate fractions


20x^2/100x^2+80x/100x^2+(-150x)/100x^2=0

We multiply all the terms by the denominator


20x^2+80x+(-150x)=0

We get rid of parentheses

20x^2+80x-150x=0

We add all the numbers together, and all the variables

20x^2-70x=0

a = 20; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·20·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*20}=\frac{0}{40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*20}=\frac{140}{40}
=3+1/2
$