(x^2-7x+24)/(-x+9)=2

Solution for (x^2-7x+24)/(-x+9)=2 equation:

(x^2-7x+24)/(-x+9)=2

We move all terms to the left:

(x^2-7x+24)/(-x+9)-(2)=0


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

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

-x!=-9

x!=-9/-1

x!=+9

x∈R


We add all the numbers together, and all the variables

(x^2-7x+24)/(-1x+9)-2=0

We multiply all the terms by the denominator


(x^2-7x+24)-2*(-1x+9)=0

We multiply parentheses

(x^2-7x+24)+2x-18=0

We get rid of parentheses

x^2-7x+2x+24-18=0

We add all the numbers together, and all the variables

x^2-5x+6=0

a = 1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·1·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*1}=\frac{6}{2}
=3
$