2x^2=4.5^2

Solution for 2x^2=4.5^2 equation:

2x^2=4.5^2

We move all terms to the left:

2x^2-(4.5^2)=0

We add all the numbers together, and all the variables

2x^2-20.25=0

a = 2; b = 0; c = -20.25;
Δ = b2-4ac
Δ = 02-4·2·(-20.25)
Δ = 162
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:

$\sqrt{\Delta}=\sqrt{162}=\sqrt{81*2}=\sqrt{81}*\sqrt{2}=9\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-9\sqrt{2}}{2*2}=\frac{0-9\sqrt{2}}{4}
=-\frac{9\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+9\sqrt{2}}{2*2}=\frac{0+9\sqrt{2}}{4}
=\frac{9\sqrt{2}}{4}
$