a+21=1/4a

Solution for a+21=1/4a equation:

a+21=1/4a

We move all terms to the left:

a+21-(1/4a)=0


Domain of the equation: 4a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

a-(+1/4a)+21=0

We get rid of parentheses

a-1/4a+21=0

We multiply all the terms by the denominator


a*4a+21*4a-1=0

Wy multiply elements

4a^2+84a-1=0

a = 4; b = 84; c = -1;
Δ = b2-4ac
Δ = 842-4·4·(-1)
Δ = 7072
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:

$\sqrt{\Delta}=\sqrt{7072}=\sqrt{16*442}=\sqrt{16}*\sqrt{442}=4\sqrt{442}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{442}}{2*4}=\frac{-84-4\sqrt{442}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{442}}{2*4}=\frac{-84+4\sqrt{442}}{8}
$