x+6/x=122

Solution for x+6/x=122 equation:

x+6/x=122

We move all terms to the left:

x+6/x-(122)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-122*x+6=0

We add all the numbers together, and all the variables

-122x+x*x+6=0

Wy multiply elements

x^2-122x+6=0

a = 1; b = -122; c = +6;
Δ = b2-4ac
Δ = -1222-4·1·6
Δ = 14860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14860}=\sqrt{4*3715}=\sqrt{4}*\sqrt{3715}=2\sqrt{3715}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122)-2\sqrt{3715}}{2*1}=\frac{122-2\sqrt{3715}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122)+2\sqrt{3715}}{2*1}=\frac{122+2\sqrt{3715}}{2}
$