6900=6x+900000/x

Solution for 6900=6x+900000/x equation:

6900=6x+900000/x

We move all terms to the left:

6900-(6x+900000/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+6x+900000/x)+6900=0

We get rid of parentheses

-6x-900000/x+6900=0

We multiply all the terms by the denominator


-6x*x+6900*x-900000=0

We add all the numbers together, and all the variables

6900x-6x*x-900000=0

Wy multiply elements

-6x^2+6900x-900000=0

a = -6; b = 6900; c = -900000;
Δ = b2-4ac
Δ = 69002-4·(-6)·(-900000)
Δ = 26010000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26010000}=5100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6900)-5100}{2*-6}=\frac{-12000}{-12}
=+1000
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6900)+5100}{2*-6}=\frac{-1800}{-12}
=+150
$