1000/x+4x=998

Solution for 1000/x+4x=998 equation:

1000/x+4x=998

We move all terms to the left:

1000/x+4x-(998)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

4x+1000/x-998=0

We multiply all the terms by the denominator


4x*x-998*x+1000=0

We add all the numbers together, and all the variables

-998x+4x*x+1000=0

Wy multiply elements

4x^2-998x+1000=0

a = 4; b = -998; c = +1000;
Δ = b2-4ac
Δ = -9982-4·4·1000
Δ = 980004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{980004}=\sqrt{4*245001}=\sqrt{4}*\sqrt{245001}=2\sqrt{245001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-998)-2\sqrt{245001}}{2*4}=\frac{998-2\sqrt{245001}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-998)+2\sqrt{245001}}{2*4}=\frac{998+2\sqrt{245001}}{8}
$