23=x-9/x=14

Solution for 23=x-9/x=14 equation:

23=x-9/x=14

We move all terms to the left:

23-(x-9/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-9/x)+23=0

We get rid of parentheses

-x+9/x+23=0

We multiply all the terms by the denominator


-x*x+23*x+9=0

We add all the numbers together, and all the variables

23x-x*x+9=0

Wy multiply elements

-1x^2+23x+9=0

a = -1; b = 23; c = +9;
Δ = b2-4ac
Δ = 232-4·(-1)·9
Δ = 565
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{565}}{2*-1}=\frac{-23-\sqrt{565}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{565}}{2*-1}=\frac{-23+\sqrt{565}}{-2}
$