-1/4a-4=a

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

-1/4a-4=a

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4a^2-16a-1=0

a = -4; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·(-4)·(-1)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{15}}{2*-4}=\frac{16-4\sqrt{15}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{15}}{2*-4}=\frac{16+4\sqrt{15}}{-8}
$