13=12/x+x

Solution for 13=12/x+x equation:

13=12/x+x

We move all terms to the left:

13-(12/x+x)=0


Domain of the equation: x+x)!=0

x∈R


We add all the numbers together, and all the variables

-(+x+12/x)+13=0

We get rid of parentheses

-x-12/x+13=0

We multiply all the terms by the denominator


-x*x+13*x-12=0

We add all the numbers together, and all the variables

13x-x*x-12=0

Wy multiply elements

-1x^2+13x-12=0

a = -1; b = 13; c = -12;
Δ = b2-4ac
Δ = 132-4·(-1)·(-12)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-11}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+11}{2*-1}=\frac{-2}{-2}
=1
$