800/6x+1000/10x=1

Solution for 800/6x+1000/10x=1 equation:

800/6x+1000/10x=1

We move all terms to the left:

800/6x+1000/10x-(1)=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^2-1=0

We multiply all the terms by the denominator


8000x+6000x-1*60x^2=0

We add all the numbers together, and all the variables

14000x-1*60x^2=0

Wy multiply elements

-60x^2+14000x=0

a = -60; b = 14000; c = 0;
Δ = b2-4ac
Δ = 140002-4·(-60)·0
Δ = 196000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196000000}=14000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14000)-14000}{2*-60}=\frac{-28000}{-120}
=233+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14000)+14000}{2*-60}=\frac{0}{-120}
=0
$