20x=500/x+4

Solution for 20x=500/x+4 equation:

20x=500/x+4

We move all terms to the left:

20x-(500/x+4)=0


Domain of the equation: x+4)!=0

x∈R


We get rid of parentheses

20x-500/x-4=0

We multiply all the terms by the denominator


20x*x-4*x-500=0

We add all the numbers together, and all the variables

-4x+20x*x-500=0

Wy multiply elements

20x^2-4x-500=0

a = 20; b = -4; c = -500;
Δ = b2-4ac
Δ = -42-4·20·(-500)
Δ = 40016
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:

$\sqrt{\Delta}=\sqrt{40016}=\sqrt{16*2501}=\sqrt{16}*\sqrt{2501}=4\sqrt{2501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2501}}{2*20}=\frac{4-4\sqrt{2501}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2501}}{2*20}=\frac{4+4\sqrt{2501}}{40}
$