X+14=12/x+2

Solution for X+14=12/x+2 equation:

X+14=12/X+2

We move all terms to the left:

X+14-(12/X+2)=0


Domain of the equation: X+2)!=0

X∈R


We get rid of parentheses

X-12/X-2+14=0

We multiply all the terms by the denominator


X*X-2*X+14*X-12=0

We add all the numbers together, and all the variables

12X+X*X-12=0

Wy multiply elements

X^2+12X-12=0

a = 1; b = 12; c = -12;
Δ = b2-4ac
Δ = 122-4·1·(-12)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{3}}{2*1}=\frac{-12-8\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{3}}{2*1}=\frac{-12+8\sqrt{3}}{2}
$