16=a-1/5a

Solution for 16=a-1/5a equation:

16=a-1/5a

We move all terms to the left:

16-(a-1/5a)=0


Domain of the equation: 5a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

-(+a-1/5a)+16=0

We get rid of parentheses

-a+1/5a+16=0

We multiply all the terms by the denominator


-a*5a+16*5a+1=0

Wy multiply elements

-5a^2+80a+1=0

a = -5; b = 80; c = +1;
Δ = b2-4ac
Δ = 802-4·(-5)·1
Δ = 6420
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:

$\sqrt{\Delta}=\sqrt{6420}=\sqrt{4*1605}=\sqrt{4}*\sqrt{1605}=2\sqrt{1605}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-2\sqrt{1605}}{2*-5}=\frac{-80-2\sqrt{1605}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+2\sqrt{1605}}{2*-5}=\frac{-80+2\sqrt{1605}}{-10}
$