x=-10/x+9

Solution for x=-10/x+9 equation:

x=-10/x+9

We move all terms to the left:

x-(-10/x+9)=0


Domain of the equation: x+9)!=0

x∈R


We get rid of parentheses

x+10/x-9=0

We multiply all the terms by the denominator


x*x-9*x+10=0

We add all the numbers together, and all the variables

-9x+x*x+10=0

Wy multiply elements

x^2-9x+10=0

a = 1; b = -9; c = +10;
Δ = b2-4ac
Δ = -92-4·1·10
Δ = 41
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{-(-9)-\sqrt{41}}{2*1}=\frac{9-\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{41}}{2*1}=\frac{9+\sqrt{41}}{2}
$