13/x=14-x

Solution for 13/x=14-x equation:

13/x=14-x

We move all terms to the left:

13/x-(14-x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

13/x-(-1x+14)=0

We get rid of parentheses

13/x+1x-14=0

We multiply all the terms by the denominator


1x*x-14*x+13=0

We add all the numbers together, and all the variables

-14x+1x*x+13=0

Wy multiply elements

x^2-14x+13=0

a = 1; b = -14; c = +13;
Δ = b2-4ac
Δ = -142-4·1·13
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-12}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+12}{2*1}=\frac{26}{2}
=13
$