3x^2=27^3

Solution for 3x^2=27^3 equation:

3x^2=27^3

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2-19683=0

a = 3; b = 0; c = -19683;
Δ = b2-4ac
Δ = 02-4·3·(-19683)
Δ = 236196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{236196}=486$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-486}{2*3}=\frac{-486}{6}
=-81
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+486}{2*3}=\frac{486}{6}
=81
$