a=10+1/4a

Solution for a=10+1/4a equation:

a=10+1/4a

We move all terms to the left:

a-(10+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+10)=0

We get rid of parentheses

a-1/4a-10=0

We multiply all the terms by the denominator


a*4a-10*4a-1=0

Wy multiply elements

4a^2-40a-1=0

a = 4; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·4·(-1)
Δ = 1616
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:

$\sqrt{\Delta}=\sqrt{1616}=\sqrt{16*101}=\sqrt{16}*\sqrt{101}=4\sqrt{101}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{101}}{2*4}=\frac{40-4\sqrt{101}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{101}}{2*4}=\frac{40+4\sqrt{101}}{8}
$