1/3*3x-6+2x+3=9

Solution for 1/3*3x-6+2x+3=9 equation:

1/3*3x-6+2x+3=9

We move all terms to the left:

1/3*3x-6+2x+3-(9)=0


Domain of the equation: 3*3x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/3*3x-12=0

We multiply all the terms by the denominator


2x*3*3x-12*3*3x+1=0

Wy multiply elements

18x^2*3-108x*3+1=0

Wy multiply elements

54x^2-324x+1=0

a = 54; b = -324; c = +1;
Δ = b2-4ac
Δ = -3242-4·54·1
Δ = 104760
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:

$\sqrt{\Delta}=\sqrt{104760}=\sqrt{36*2910}=\sqrt{36}*\sqrt{2910}=6\sqrt{2910}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-6\sqrt{2910}}{2*54}=\frac{324-6\sqrt{2910}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+6\sqrt{2910}}{2*54}=\frac{324+6\sqrt{2910}}{108}
$