1/3(a+3)(a-3)=2a-6

Solution for 1/3(a+3)(a-3)=2a-6 equation:

1/3(a+3)(a-3)=2a-6

We move all terms to the left:

1/3(a+3)(a-3)-(2a-6)=0


Domain of the equation: 3(a+3)(a-3)!=0

a∈R


We use the square of the difference formula

a^2-(2a-6)-9=0

We get rid of parentheses

a^2-2a+6-9=0

We add all the numbers together, and all the variables

a^2-2a-3=0

a = 1; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·1·(-3)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*1}=\frac{-2}{2}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*1}=\frac{6}{2}
=3
$