(6*8a)(6*8a)-36=1

Solution for (6*8a)(6*8a)-36=1 equation:

(6*8a)(6*8a)-36=1

We move all terms to the left:

(6*8a)(6*8a)-36-(1)=0

We add all the numbers together, and all the variables

(+6*8a)(+6*8a)-36-1=0

We add all the numbers together, and all the variables

(+6*8a)(+6*8a)-37=0

We multiply parentheses ..

(+2304a^2)-37=0

We get rid of parentheses

2304a^2-37=0

a = 2304; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·2304·(-37)
Δ = 340992
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:

$\sqrt{\Delta}=\sqrt{340992}=\sqrt{9216*37}=\sqrt{9216}*\sqrt{37}=96\sqrt{37}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96\sqrt{37}}{2*2304}=\frac{0-96\sqrt{37}}{4608}
=-\frac{96\sqrt{37}}{4608}
=-\frac{\sqrt{37}}{48}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96\sqrt{37}}{2*2304}=\frac{0+96\sqrt{37}}{4608}
=\frac{96\sqrt{37}}{4608}
=\frac{\sqrt{37}}{48}
$