1/a^2=80

Solution for 1/a^2=80 equation:

1/a^2=80

We move all terms to the left:

1/a^2-(80)=0


Domain of the equation: a^2!=0

a^2!=0/

a^2!=√0

a!=0

a∈R


We multiply all the terms by the denominator


-80*a^2+1=0

We add all the numbers together, and all the variables

-80a^2+1=0

a = -80; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-80)·1
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*-80}=\frac{0-8\sqrt{5}}{-160}
=-\frac{8\sqrt{5}}{-160}
=-\frac{\sqrt{5}}{-20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*-80}=\frac{0+8\sqrt{5}}{-160}
=\frac{8\sqrt{5}}{-160}
=\frac{\sqrt{5}}{-20}
$