(4x+8)=20/x

Solution for (4x+8)=20/x equation:

(4x+8)=20/x

We move all terms to the left:

(4x+8)-(20/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(4x+8)-(+20/x)=0

We get rid of parentheses

4x-20/x+8=0

We multiply all the terms by the denominator


4x*x+8*x-20=0

We add all the numbers together, and all the variables

8x+4x*x-20=0

Wy multiply elements

4x^2+8x-20=0

a = 4; b = 8; c = -20;
Δ = b2-4ac
Δ = 82-4·4·(-20)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{6}}{2*4}=\frac{-8-8\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{6}}{2*4}=\frac{-8+8\sqrt{6}}{8}
$