3x^2-27=9x+27

Solution for 3x^2-27=9x+27 equation:

3x^2-27=9x+27

We move all terms to the left:

3x^2-27-(9x+27)=0

We get rid of parentheses

3x^2-9x-27-27=0

We add all the numbers together, and all the variables

3x^2-9x-54=0

a = 3; b = -9; c = -54;
Δ = b2-4ac
Δ = -92-4·3·(-54)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-27}{2*3}=\frac{-18}{6}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+27}{2*3}=\frac{36}{6}
=6
$