2a+1/a=25

Solution for 2a+1/a=25 equation:

2a+1/a=25

We move all terms to the left:

2a+1/a-(25)=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


2a*a-25*a+1=0

We add all the numbers together, and all the variables

-25a+2a*a+1=0

Wy multiply elements

2a^2-25a+1=0

a = 2; b = -25; c = +1;
Δ = b2-4ac
Δ = -252-4·2·1
Δ = 617
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{-(-25)-\sqrt{617}}{2*2}=\frac{25-\sqrt{617}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{617}}{2*2}=\frac{25+\sqrt{617}}{4}
$