-1/4a-4=4a

Solution for -1/4a-4=4a equation:

-1/4a-4=4a

We move all terms to the left:

-1/4a-4-(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-4=0

We multiply all the terms by the denominator


-4a*4a-4*4a-1=0

Wy multiply elements

-16a^2-16a-1=0

a = -16; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·(-16)·(-1)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{3}}{2*-16}=\frac{16-8\sqrt{3}}{-32}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{3}}{2*-16}=\frac{16+8\sqrt{3}}{-32}
$