a+2/a=90

Solution for a+2/a=90 equation:

a+2/a=90

We move all terms to the left:

a+2/a-(90)=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


a*a-90*a+2=0

We add all the numbers together, and all the variables

-90a+a*a+2=0

Wy multiply elements

a^2-90a+2=0

a = 1; b = -90; c = +2;
Δ = b2-4ac
Δ = -902-4·1·2
Δ = 8092
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:

$\sqrt{\Delta}=\sqrt{8092}=\sqrt{1156*7}=\sqrt{1156}*\sqrt{7}=34\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-34\sqrt{7}}{2*1}=\frac{90-34\sqrt{7}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+34\sqrt{7}}{2*1}=\frac{90+34\sqrt{7}}{2}
$