1/4a=4a

Solution for 1/4a=4a equation:

1/4a=4a

We move all terms to the left:

1/4a-(4a)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

-4a+1/4a=0

We multiply all the terms by the denominator


-4a*4a+1=0

Wy multiply elements

-16a^2+1=0

a = -16; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-16)·1
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*-16}=\frac{-8}{-32}
=1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*-16}=\frac{8}{-32}
=-1/4
$