Y^3-27=9y^2-27

Solution for Y^3-27=9y^2-27 equation:

^3-27=9Y^2-27

We move all terms to the left:

^3-27-(9Y^2-27)=0

We add all the numbers together, and all the variables

-(9Y^2-27)=0

We get rid of parentheses

-9Y^2+27=0

a = -9; b = 0; c = +27;
Δ = b2-4ac
Δ = 02-4·(-9)·27
Δ = 972
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*-9}=\frac{0-18\sqrt{3}}{-18}
=-\frac{18\sqrt{3}}{-18}
=-\frac{\sqrt{3}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*-9}=\frac{0+18\sqrt{3}}{-18}
=\frac{18\sqrt{3}}{-18}
=\frac{\sqrt{3}}{-1}
$