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

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

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


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

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

2x^2+x!=6

x∈R


We multiply all the terms by the denominator


(x^2-x-6)=0

We get rid of parentheses

x^2-x-6=0

We add all the numbers together, and all the variables

x^2-1x-6=0

a = 1; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·1·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*1}=\frac{6}{2}
=3
$