1/8x=1/3x-10

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

1/8x=1/3x-10

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 3x-10)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


3x/24x^2+(-8x)/24x^2+10=0

We multiply all the terms by the denominator


3x+(-8x)+10*24x^2=0

Wy multiply elements

240x^2+3x+(-8x)=0

We get rid of parentheses

240x^2+3x-8x=0

We add all the numbers together, and all the variables

240x^2-5x=0

a = 240; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·240·0
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*240}=\frac{0}{480}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*240}=\frac{10}{480}
=1/48
$