x-20=20/3x

Solution for x-20=20/3x equation:

x-20=20/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-20/3x-20=0

We multiply all the terms by the denominator


x*3x-20*3x-20=0

Wy multiply elements

3x^2-60x-20=0

a = 3; b = -60; c = -20;
Δ = b2-4ac
Δ = -602-4·3·(-20)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-16\sqrt{15}}{2*3}=\frac{60-16\sqrt{15}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+16\sqrt{15}}{2*3}=\frac{60+16\sqrt{15}}{6}
$