5x+50+2000/x=10x+50

Solution for 5x+50+2000/x=10x+50 equation:

5x+50+2000/x=10x+50

We move all terms to the left:

5x+50+2000/x-(10x+50)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

5x+2000/x-10x-50+50=0

We multiply all the terms by the denominator


5x*x-10x*x-50*x+50*x+2000=0

We add all the numbers together, and all the variables

5x*x-10x*x+2000=0

Wy multiply elements

5x^2-10x^2+2000=0

We add all the numbers together, and all the variables

-5x^2+2000=0

a = -5; b = 0; c = +2000;
Δ = b2-4ac
Δ = 02-4·(-5)·2000
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200}{2*-5}=\frac{-200}{-10}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200}{2*-5}=\frac{200}{-10}
=-20
$