(3x^2-27)/(x-3)=0

Solution for (3x^2-27)/(x-3)=0 equation:

(3x^2-27)/(x-3)=0


Domain of the equation: (x-3)!=0

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

x!=3

x∈R


We multiply all the terms by the denominator


(3x^2-27)=0

We get rid of parentheses

3x^2-27=0

a = 3; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·3·(-27)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18}{2*3}=\frac{18}{6}
=3
$