(x+3)(122/x+12)=122

Solution for (x+3)(122/x+12)=122 equation:

(x+3)(122/x+12)=122

We move all terms to the left:

(x+3)(122/x+12)-(122)=0


Domain of the equation: x+12)!=0

x∈R


We multiply parentheses ..

(+122x^2+12x+366x+36)-122=0

We get rid of parentheses

122x^2+12x+366x+36-122=0

We add all the numbers together, and all the variables

122x^2+378x-86=0

a = 122; b = 378; c = -86;
Δ = b2-4ac
Δ = 3782-4·122·(-86)
Δ = 184852
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:

$\sqrt{\Delta}=\sqrt{184852}=\sqrt{4*46213}=\sqrt{4}*\sqrt{46213}=2\sqrt{46213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(378)-2\sqrt{46213}}{2*122}=\frac{-378-2\sqrt{46213}}{244}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(378)+2\sqrt{46213}}{2*122}=\frac{-378+2\sqrt{46213}}{244}
$