(100/x+2)(x-5)=105

Solution for (100/x+2)(x-5)=105 equation:

(100/x+2)(x-5)=105

We move all terms to the left:

(100/x+2)(x-5)-(105)=0


Domain of the equation: x+2)(x-5)!=0

x∈R


We multiply parentheses ..

(+100x^2-500x+2x-10)-105=0

We get rid of parentheses

100x^2-500x+2x-10-105=0

We add all the numbers together, and all the variables

100x^2-498x-115=0

a = 100; b = -498; c = -115;
Δ = b2-4ac
Δ = -4982-4·100·(-115)
Δ = 294004
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:

$\sqrt{\Delta}=\sqrt{294004}=\sqrt{4*73501}=\sqrt{4}*\sqrt{73501}=2\sqrt{73501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-498)-2\sqrt{73501}}{2*100}=\frac{498-2\sqrt{73501}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-498)+2\sqrt{73501}}{2*100}=\frac{498+2\sqrt{73501}}{200}
$