(x^2-7x+12)/(x^2-x-6)=0

Solution for (x^2-7x+12)/(x^2-x-6)=0 equation:

(x^2-7x+12)/(x^2-x-6)=0


Domain of the equation: (x^2-x-6)!=0

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

x^2-x!=6

x∈R


We multiply all the terms by the denominator


(x^2-7x+12)=0

We get rid of parentheses

x^2-7x+12=0

a = 1; b = -7; c = +12;
Δ = b2-4ac
Δ = -72-4·1·12
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{-(-7)-1}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*1}=\frac{8}{2}
=4
$