(x)(2)=(3)(27)

Solution for (x)(2)=(3)(27) equation:

(x)(2)=(3)(27)

We move all terms to the left:

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

determiningTheFunctionDomain
x2-327=0

We add all the numbers together, and all the variables

x^2-327=0

a = 1; b = 0; c = -327;
Δ = b2-4ac
Δ = 02-4·1·(-327)
Δ = 1308
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1308}=\sqrt{4*327}=\sqrt{4}*\sqrt{327}=2\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{327}}{2*1}=\frac{0-2\sqrt{327}}{2}
=-\frac{2\sqrt{327}}{2}
=-\sqrt{327}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{327}}{2*1}=\frac{0+2\sqrt{327}}{2}
=\frac{2\sqrt{327}}{2}
=\sqrt{327}
$