(2x)^2=126^2

Solution for (2x)^2=126^2 equation:

(2x)^2=126^2

We move all terms to the left:

(2x)^2-(126^2)=0

We add all the numbers together, and all the variables

2x^2-15876=0

a = 2; b = 0; c = -15876;
Δ = b2-4ac
Δ = 02-4·2·(-15876)
Δ = 127008
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:

$\sqrt{\Delta}=\sqrt{127008}=\sqrt{63504*2}=\sqrt{63504}*\sqrt{2}=252\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-252\sqrt{2}}{2*2}=\frac{0-252\sqrt{2}}{4}
=-\frac{252\sqrt{2}}{4}
=-63\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+252\sqrt{2}}{2*2}=\frac{0+252\sqrt{2}}{4}
=\frac{252\sqrt{2}}{4}
=63\sqrt{2}
$