a+1/5a=55

Solution for a+1/5a=55 equation:

a+1/5a=55

We move all terms to the left:

a+1/5a-(55)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We multiply all the terms by the denominator


a*5a-55*5a+1=0

Wy multiply elements

5a^2-275a+1=0

a = 5; b = -275; c = +1;
Δ = b2-4ac
Δ = -2752-4·5·1
Δ = 75605
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-275)-\sqrt{75605}}{2*5}=\frac{275-\sqrt{75605}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-275)+\sqrt{75605}}{2*5}=\frac{275+\sqrt{75605}}{10}
$