X+2=24/x+6

Solution for X+2=24/x+6 equation:

X+2=24/X+6

We move all terms to the left:

X+2-(24/X+6)=0


Domain of the equation: X+6)!=0

X∈R


We get rid of parentheses

X-24/X-6+2=0

We multiply all the terms by the denominator


X*X-6*X+2*X-24=0

We add all the numbers together, and all the variables

-4X+X*X-24=0

Wy multiply elements

X^2-4X-24=0

a = 1; b = -4; c = -24;
Δ = b2-4ac
Δ = -42-4·1·(-24)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*1}=\frac{4-4\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*1}=\frac{4+4\sqrt{7}}{2}
$