2x^2=13.5^2

Solution for 2x^2=13.5^2 equation:

2x^2=13.5^2

We move all terms to the left:

2x^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}
$