(3000000/x)+20x=30000

Solution for (3000000/x)+20x=30000 equation:

(3000000/x)+20x=30000

We move all terms to the left:

(3000000/x)+20x-(30000)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3000000/x)+20x-30000=0

We add all the numbers together, and all the variables

20x+(+3000000/x)-30000=0

We get rid of parentheses

20x+3000000/x-30000=0

We multiply all the terms by the denominator


20x*x-30000*x+3000000=0

We add all the numbers together, and all the variables

-30000x+20x*x+3000000=0

Wy multiply elements

20x^2-30000x+3000000=0

a = 20; b = -30000; c = +3000000;
Δ = b2-4ac
Δ = -300002-4·20·3000000
Δ = 660000000
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:

$\sqrt{\Delta}=\sqrt{660000000}=\sqrt{4000000*165}=\sqrt{4000000}*\sqrt{165}=2000\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30000)-2000\sqrt{165}}{2*20}=\frac{30000-2000\sqrt{165}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30000)+2000\sqrt{165}}{2*20}=\frac{30000+2000\sqrt{165}}{40}
$