9=5/x+2-x

Solution for 9=5/x+2-x equation:

9=5/x+2-x

We move all terms to the left:

9-(5/x+2-x)=0


Domain of the equation: x+2-x)!=0

We move all terms containing x to the left, all other terms to the right

x-x)!=-2

x∈R


We add all the numbers together, and all the variables

-(-1x+5/x+2)+9=0

We get rid of parentheses

1x-5/x-2+9=0

We multiply all the terms by the denominator


1x*x-2*x+9*x-5=0

We add all the numbers together, and all the variables

7x+1x*x-5=0

Wy multiply elements

x^2+7x-5=0

a = 1; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·1·(-5)
Δ = 69
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{-(7)-\sqrt{69}}{2*1}=\frac{-7-\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{69}}{2*1}=\frac{-7+\sqrt{69}}{2}
$