1/10x=1/8x+300

Solution for 1/10x=1/8x+300 equation:

1/10x=1/8x+300

We move all terms to the left:

1/10x-(1/8x+300)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 8x+300)!=0

x∈R


We get rid of parentheses

1/10x-1/8x-300=0

We calculate fractions


8x/80x^2+(-10x)/80x^2-300=0

We multiply all the terms by the denominator


8x+(-10x)-300*80x^2=0

Wy multiply elements

-24000x^2+8x+(-10x)=0

We get rid of parentheses

-24000x^2+8x-10x=0

We add all the numbers together, and all the variables

-24000x^2-2x=0

a = -24000; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-24000)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-24000}=\frac{0}{-48000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-24000}=\frac{4}{-48000}
=-1/12000
$