1/5x-3/8x=1/10

Solution for 1/5x-3/8x=1/10 equation:

1/5x-3/8x=1/10

We move all terms to the left:

1/5x-3/8x-(1/10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-3/8x-(+1/10)=0

We get rid of parentheses

1/5x-3/8x-1/10=0

We calculate fractions


(-320x^2)/400x^2+80x/400x^2+(-150x)/400x^2=0

We multiply all the terms by the denominator


(-320x^2)+80x+(-150x)=0

We get rid of parentheses

-320x^2+80x-150x=0

We add all the numbers together, and all the variables

-320x^2-70x=0

a = -320; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·(-320)·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*-320}=\frac{0}{-640}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*-320}=\frac{140}{-640}
=-7/32
$