81x^2-1=80

Solution for 81x^2-1=80 equation:

81x^2-1=80

We move all terms to the left:

81x^2-1-(80)=0

We add all the numbers together, and all the variables

81x^2-81=0

a = 81; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·81·(-81)
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-162}{2*81}=\frac{-162}{162}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+162}{2*81}=\frac{162}{162}
=1
$