81x2-1=27

Solution for 81x2-1=27 equation:

81x^2-1=27

We move all terms to the left:

81x^2-1-(27)=0

We add all the numbers together, and all the variables

81x^2-28=0

a = 81; b = 0; c = -28;
Δ = b2-4ac
Δ = 02-4·81·(-28)
Δ = 9072
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:

$\sqrt{\Delta}=\sqrt{9072}=\sqrt{1296*7}=\sqrt{1296}*\sqrt{7}=36\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{7}}{2*81}=\frac{0-36\sqrt{7}}{162}
=-\frac{36\sqrt{7}}{162}
=-\frac{2\sqrt{7}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{7}}{2*81}=\frac{0+36\sqrt{7}}{162}
=\frac{36\sqrt{7}}{162}
=\frac{2\sqrt{7}}{9}
$