x-20=1/3x

Solution for x-20=1/3x equation:

x-20=1/3x

We move all terms to the left:

x-20-(1/3x)=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-(+1/3x)-20=0

We get rid of parentheses

x-1/3x-20=0

We multiply all the terms by the denominator


x*3x-20*3x-1=0

Wy multiply elements

3x^2-60x-1=0

a = 3; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·3·(-1)
Δ = 3612
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:

$\sqrt{\Delta}=\sqrt{3612}=\sqrt{4*903}=\sqrt{4}*\sqrt{903}=2\sqrt{903}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{903}}{2*3}=\frac{60-2\sqrt{903}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{903}}{2*3}=\frac{60+2\sqrt{903}}{6}
$