-10/x-9=x-2

Solution for -10/x-9=x-2 equation:

-10/x-9=x-2

We move all terms to the left:

-10/x-9-(x-2)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

-10/x-x+2-9=0

We multiply all the terms by the denominator


-x*x+2*x-9*x-10=0

We add all the numbers together, and all the variables

-7x-x*x-10=0

Wy multiply elements

-1x^2-7x-10=0

a = -1; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·(-1)·(-10)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*-1}=\frac{4}{-2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*-1}=\frac{10}{-2}
=-5
$