x+8/4=18/x+2

Solution for x+8/4=18/x+2 equation:

x+8/4=18/x+2

We move all terms to the left:

x+8/4-(18/x+2)=0


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

x∈R


We add all the numbers together, and all the variables

x-(18/x+2)+2=0

We get rid of parentheses

x-18/x-2+2=0

We multiply all the terms by the denominator


x*x-2*x+2*x-18=0

We add all the numbers together, and all the variables

x*x-18=0

Wy multiply elements

x^2-18=0

a = 1; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·1·(-18)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*1}=\frac{0-6\sqrt{2}}{2}
=-\frac{6\sqrt{2}}{2}
=-3\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*1}=\frac{0+6\sqrt{2}}{2}
=\frac{6\sqrt{2}}{2}
=3\sqrt{2}
$