800/6x-1000/10x=2

Solution for 800/6x-1000/10x=2 equation:

800/6x-1000/10x=2

We move all terms to the left:

800/6x-1000/10x-(2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We calculate fractions


8000x/60x^2+(-6000x)/60x^2-2=0

We multiply all the terms by the denominator


8000x+(-6000x)-2*60x^2=0

Wy multiply elements

-120x^2+8000x+(-6000x)=0

We get rid of parentheses

-120x^2+8000x-6000x=0

We add all the numbers together, and all the variables

-120x^2+2000x=0

a = -120; b = 2000; c = 0;
Δ = b2-4ac
Δ = 20002-4·(-120)·0
Δ = 4000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4000000}=2000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2000)-2000}{2*-120}=\frac{-4000}{-240}
=16+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2000)+2000}{2*-120}=\frac{0}{-240}
=0
$