X=108/x+3

Solution for X=108/x+3 equation:

X=108/X+3

We move all terms to the left:

X-(108/X+3)=0


Domain of the equation: X+3)!=0

X∈R


We get rid of parentheses

X-108/X-3=0

We multiply all the terms by the denominator


X*X-3*X-108=0

We add all the numbers together, and all the variables

-3X+X*X-108=0

Wy multiply elements

X^2-3X-108=0

a = 1; b = -3; c = -108;
Δ = b2-4ac
Δ = -32-4·1·(-108)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*1}=\frac{-18}{2}
=-9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*1}=\frac{24}{2}
=12
$