5x-1000=400/x

Solution for 5x-1000=400/x equation:

5x-1000=400/x

We move all terms to the left:

5x-1000-(400/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

5x-(+400/x)-1000=0

We get rid of parentheses

5x-400/x-1000=0

We multiply all the terms by the denominator


5x*x-1000*x-400=0

We add all the numbers together, and all the variables

-1000x+5x*x-400=0

Wy multiply elements

5x^2-1000x-400=0

a = 5; b = -1000; c = -400;
Δ = b2-4ac
Δ = -10002-4·5·(-400)
Δ = 1008000
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:

$\sqrt{\Delta}=\sqrt{1008000}=\sqrt{14400*70}=\sqrt{14400}*\sqrt{70}=120\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-120\sqrt{70}}{2*5}=\frac{1000-120\sqrt{70}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+120\sqrt{70}}{2*5}=\frac{1000+120\sqrt{70}}{10}
$