20=3x+8/x=

Solution for 20=3x+8/x= equation:

20=3x+8/x=

We move all terms to the left:

20-(3x+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

-(+3x+8/x)+20=0

We get rid of parentheses

-3x-8/x+20=0

We multiply all the terms by the denominator


-3x*x+20*x-8=0

We add all the numbers together, and all the variables

20x-3x*x-8=0

Wy multiply elements

-3x^2+20x-8=0

a = -3; b = 20; c = -8;
Δ = b2-4ac
Δ = 202-4·(-3)·(-8)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{19}}{2*-3}=\frac{-20-4\sqrt{19}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{19}}{2*-3}=\frac{-20+4\sqrt{19}}{-6}
$