x^2+13.5^2=(3x)^2

Solution for x^2+13.5^2=(3x)^2 equation:

x^2+13.5^2=(3x)^2

We move all terms to the left:

x^2+13.5^2-((3x)^2)=0

determiningTheFunctionDomain
x^2-3x^2+13.5^2=0

We add all the numbers together, and all the variables

-2x^2+182.25=0

a = -2; b = 0; c = +182.25;
Δ = b2-4ac
Δ = 02-4·(-2)·182.25
Δ = 1458
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:

$\sqrt{\Delta}=\sqrt{1458}=\sqrt{729*2}=\sqrt{729}*\sqrt{2}=27\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-27\sqrt{2}}{2*-2}=\frac{0-27\sqrt{2}}{-4}
=-\frac{27\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+27\sqrt{2}}{2*-2}=\frac{0+27\sqrt{2}}{-4}
=\frac{27\sqrt{2}}{-4}
$