(X^2+x-12)/(6x^2-54)=0

Solution for (X^2+x-12)/(6x^2-54)=0 equation:

(X^2+X-12)/(6X^2-54)=0


Domain of the equation: (6X^2-54)!=0

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

6X^2!=54

X^2!=54/6

X^2!=√9

X!=3

X∈R


We multiply all the terms by the denominator


(X^2+X-12)=0

We get rid of parentheses

X^2+X-12=0

a = 1; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·1·(-12)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*1}=\frac{-8}{2}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*1}=\frac{6}{2}
=3
$