1/a^2=4

Solution for 1/a^2=4 equation:

1/a^2=4

We move all terms to the left:

1/a^2-(4)=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


-4*a^2+1=0

We add all the numbers together, and all the variables

-4a^2+1=0

a = -4; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-4)·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-4}=\frac{-4}{-8}
=1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-4}=\frac{4}{-8}
=-1/2
$