)2/3x=x-20

Solution for )2/3x=x-20 equation:

)2/3x=x-20

We move all terms to the left:

)2/3x-(x-20)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

)2/3x-x+20=0

We multiply all the terms by the denominator


)2-x*3x+20*3x=0

determiningTheFunctionDomain
-x*3x+20*3x+)2=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-3x^2+60x=0

a = -3; b = 60; c = 0;
Δ = b2-4ac
Δ = 602-4·(-3)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-60}{2*-3}=\frac{-120}{-6}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+60}{2*-3}=\frac{0}{-6}
=0
$