2x^2=55^2

Solution for 2x^2=55^2 equation:

2x^2=55^2

We move all terms to the left:

2x^2-(55^2)=0

We add all the numbers together, and all the variables

2x^2-3025=0

a = 2; b = 0; c = -3025;
Δ = b2-4ac
Δ = 02-4·2·(-3025)
Δ = 24200
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:

$\sqrt{\Delta}=\sqrt{24200}=\sqrt{12100*2}=\sqrt{12100}*\sqrt{2}=110\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-110\sqrt{2}}{2*2}=\frac{0-110\sqrt{2}}{4}
=-\frac{110\sqrt{2}}{4}
=-\frac{55\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+110\sqrt{2}}{2*2}=\frac{0+110\sqrt{2}}{4}
=\frac{110\sqrt{2}}{4}
=\frac{55\sqrt{2}}{2}
$