2x^2=20.5^2

Solution for 2x^2=20.5^2 equation:

2x^2=20.5^2

We move all terms to the left:

2x^2-(20.5^2)=0

We add all the numbers together, and all the variables

2x^2-420.25=0

a = 2; b = 0; c = -420.25;
Δ = b2-4ac
Δ = 02-4·2·(-420.25)
Δ = 3362
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:

$\sqrt{\Delta}=\sqrt{3362}=\sqrt{1681*2}=\sqrt{1681}*\sqrt{2}=41\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-41\sqrt{2}}{2*2}=\frac{0-41\sqrt{2}}{4}
=-\frac{41\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+41\sqrt{2}}{2*2}=\frac{0+41\sqrt{2}}{4}
=\frac{41\sqrt{2}}{4}
$