2x^2=42^2

Solution for 2x^2=42^2 equation:

2x^2=42^2

We move all terms to the left:

2x^2-(42^2)=0

We add all the numbers together, and all the variables

2x^2-1764=0

a = 2; b = 0; c = -1764;
Δ = b2-4ac
Δ = 02-4·2·(-1764)
Δ = 14112
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:

$\sqrt{\Delta}=\sqrt{14112}=\sqrt{7056*2}=\sqrt{7056}*\sqrt{2}=84\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84\sqrt{2}}{2*2}=\frac{0-84\sqrt{2}}{4}
=-\frac{84\sqrt{2}}{4}
=-21\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84\sqrt{2}}{2*2}=\frac{0+84\sqrt{2}}{4}
=\frac{84\sqrt{2}}{4}
=21\sqrt{2}
$