6a^2-54=(a-3)(a+3)

Solution for 6a^2-54=(a-3)(a+3) equation:

6a^2-54=(a-3)(a+3)

We move all terms to the left:

6a^2-54-((a-3)(a+3))=0

We use the square of the difference formula

6a^2+a^2+9-54=0

We add all the numbers together, and all the variables

7a^2-45=0

a = 7; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·7·(-45)
Δ = 1260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{35}}{2*7}=\frac{0-6\sqrt{35}}{14}
=-\frac{6\sqrt{35}}{14}
=-\frac{3\sqrt{35}}{7}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{35}}{2*7}=\frac{0+6\sqrt{35}}{14}
=\frac{6\sqrt{35}}{14}
=\frac{3\sqrt{35}}{7}
$