4x-20=8/x

Solution for 4x-20=8/x equation:

4x-20=8/x

We move all terms to the left:

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

We get rid of parentheses

4x-8/x-20=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

4x^2-20x-8=0

a = 4; b = -20; c = -8;
Δ = b2-4ac
Δ = -202-4·4·(-8)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{33}}{2*4}=\frac{20-4\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{33}}{2*4}=\frac{20+4\sqrt{33}}{8}
$