12=x+8/x

Solution for 12=x+8/x equation:

12=x+8/x

We move all terms to the left:

12-(x+8/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+8/x)+12=0

We get rid of parentheses

-x-8/x+12=0

We multiply all the terms by the denominator


-x*x+12*x-8=0

We add all the numbers together, and all the variables

12x-x*x-8=0

Wy multiply elements

-1x^2+12x-8=0

a = -1; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·(-1)·(-8)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{7}}{2*-1}=\frac{-12-4\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{7}}{2*-1}=\frac{-12+4\sqrt{7}}{-2}
$