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

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

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

We move all terms to the left:

4(x-9)-((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

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

We multiply parentheses

4x-((1/3x+9))-36=0

We multiply all the terms by the denominator


4x*3x-36*3x+9))-((1+9))=0

We add all the numbers together, and all the variables

4x*3x-36*3x+9))-(10)=0

We add all the numbers together, and all the variables

4x*3x-36*3x=0

Wy multiply elements

12x^2-108x=0

a = 12; b = -108; c = 0;
Δ = b2-4ac
Δ = -1082-4·12·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-108}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+108}{2*12}=\frac{216}{24}
=9
$