400/x=1200+x/800x

Solution for 400/x=1200+x/800x equation:

400/x=1200+x/800x

We move all terms to the left:

400/x-(1200+x/800x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 800x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

400/x-(x/800x+1200)=0

We get rid of parentheses

400/x-x/800x-1200=0

We calculate fractions


(-1x^2)/800x^2+320000x/800x^2-1200=0

We multiply all the terms by the denominator


(-1x^2)+320000x-1200*800x^2=0

Wy multiply elements

(-1x^2)-960000x^2+320000x=0

We get rid of parentheses

-1x^2-960000x^2+320000x=0

We add all the numbers together, and all the variables

-960001x^2+320000x=0

a = -960001; b = 320000; c = 0;
Δ = b2-4ac
Δ = 3200002-4·(-960001)·0
Δ = 102400000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400000000}=320000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(320000)-320000}{2*-960001}=\frac{-640000}{-1920002}
=320000/960001
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(320000)+320000}{2*-960001}=\frac{0}{-1920002}
=0
$