(x-9)=4(9+1/3x)

Solution for (x-9)=4(9+1/3x) equation:

(x-9)=4(9+1/3x)

We move all terms to the left:

(x-9)-(4(9+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-9)-(4(1/3x+9))=0

We get rid of parentheses

x-(4(1/3x+9))-9=0

We multiply all the terms by the denominator


x*3x-9*3x+9))-(4(1+9))=0

We add all the numbers together, and all the variables

x*3x-9*3x+9))-(410)=0

We add all the numbers together, and all the variables

x*3x-9*3x=0

Wy multiply elements

3x^2-27x=0

a = 3; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·3·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*3}=\frac{54}{6}
=9
$