2a(5/a)=11

Solution for 2a(5/a)=11 equation:

2a(5/a)=11

We move all terms to the left:

2a(5/a)-(11)=0


Domain of the equation: a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2a(+5/a)-11=0

We multiply parentheses

10a^2-11=0

a = 10; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·10·(-11)
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{110}}{2*10}=\frac{0-2\sqrt{110}}{20}
=-\frac{2\sqrt{110}}{20}
=-\frac{\sqrt{110}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{110}}{2*10}=\frac{0+2\sqrt{110}}{20}
=\frac{2\sqrt{110}}{20}
=\frac{\sqrt{110}}{10}
$