x+3/x=92

Solution for x+3/x=92 equation:

x+3/x=92

We move all terms to the left:

x+3/x-(92)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-92*x+3=0

We add all the numbers together, and all the variables

-92x+x*x+3=0

Wy multiply elements

x^2-92x+3=0

a = 1; b = -92; c = +3;
Δ = b2-4ac
Δ = -922-4·1·3
Δ = 8452
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:

$\sqrt{\Delta}=\sqrt{8452}=\sqrt{4*2113}=\sqrt{4}*\sqrt{2113}=2\sqrt{2113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-2\sqrt{2113}}{2*1}=\frac{92-2\sqrt{2113}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+2\sqrt{2113}}{2*1}=\frac{92+2\sqrt{2113}}{2}
$