321=x+20+2/3X

Solution for 321=x+20+2/3X equation:

321=x+20+2/3x

We move all terms to the left:

321-(x+20+2/3x)=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+2/3x+20)+321=0

We get rid of parentheses

-x-2/3x-20+321=0

We multiply all the terms by the denominator


-x*3x-20*3x+321*3x-2=0

Wy multiply elements

-3x^2-60x+963x-2=0

We add all the numbers together, and all the variables

-3x^2+903x-2=0

a = -3; b = 903; c = -2;
Δ = b2-4ac
Δ = 9032-4·(-3)·(-2)
Δ = 815385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(903)-\sqrt{815385}}{2*-3}=\frac{-903-\sqrt{815385}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(903)+\sqrt{815385}}{2*-3}=\frac{-903+\sqrt{815385}}{-6}
$