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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

9x^2+27x-12x+1=0

We add all the numbers together, and all the variables

9x^2+15x+1=0

a = 9; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·9·1
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{21}}{2*9}=\frac{-15-3\sqrt{21}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{21}}{2*9}=\frac{-15+3\sqrt{21}}{18}
$