a2-6=102

Solution for a2-6=102 equation:

a2-6=102

We move all terms to the left:

a2-6-(102)=0

We add all the numbers together, and all the variables

a^2-108=0

a = 1; b = 0; c = -108;
Δ = b2-4ac
Δ = 02-4·1·(-108)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*1}=\frac{0-12\sqrt{3}}{2}
=-\frac{12\sqrt{3}}{2}
=-6\sqrt{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*1}=\frac{0+12\sqrt{3}}{2}
=\frac{12\sqrt{3}}{2}
=6\sqrt{3}
$