a+6/a=14

Solution for a+6/a=14 equation:

a+6/a=14

We move all terms to the left:

a+6/a-(14)=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


a*a-14*a+6=0

We add all the numbers together, and all the variables

-14a+a*a+6=0

Wy multiply elements

a^2-14a+6=0

a = 1; b = -14; c = +6;
Δ = b2-4ac
Δ = -142-4·1·6
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{43}}{2*1}=\frac{14-2\sqrt{43}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{43}}{2*1}=\frac{14+2\sqrt{43}}{2}
$