14/x=9-x

Solution for 14/x=9-x equation:

14/x=9-x

We move all terms to the left:

14/x-(9-x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

14/x-(-1x+9)=0

We get rid of parentheses

14/x+1x-9=0

We multiply all the terms by the denominator


1x*x-9*x+14=0

We add all the numbers together, and all the variables

-9x+1x*x+14=0

Wy multiply elements

x^2-9x+14=0

a = 1; b = -9; c = +14;
Δ = b2-4ac
Δ = -92-4·1·14
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5}{2*1}=\frac{14}{2}
=7
$