200/x+20+2=20+5x

Solution for 200/x+20+2=20+5x equation:

200/x+20+2=20+5x

We move all terms to the left:

200/x+20+2-(20+5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

200/x-(5x+20)+20+2=0

We add all the numbers together, and all the variables

200/x-(5x+20)+22=0

We get rid of parentheses

200/x-5x-20+22=0

We multiply all the terms by the denominator


-5x*x-20*x+22*x+200=0

We add all the numbers together, and all the variables

2x-5x*x+200=0

Wy multiply elements

-5x^2+2x+200=0

a = -5; b = 2; c = +200;
Δ = b2-4ac
Δ = 22-4·(-5)·200
Δ = 4004
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:

$\sqrt{\Delta}=\sqrt{4004}=\sqrt{4*1001}=\sqrt{4}*\sqrt{1001}=2\sqrt{1001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1001}}{2*-5}=\frac{-2-2\sqrt{1001}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1001}}{2*-5}=\frac{-2+2\sqrt{1001}}{-10}
$