x^2+42=(2x)^2

Solution for x^2+42=(2x)^2 equation:

x^2+42=(2x)^2

We move all terms to the left:

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

determiningTheFunctionDomain
x^2-2x^2+42=0

We add all the numbers together, and all the variables

-1x^2+42=0

a = -1; b = 0; c = +42;
Δ = b2-4ac
Δ = 02-4·(-1)·42
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*-1}=\frac{0-2\sqrt{42}}{-2}
=-\frac{2\sqrt{42}}{-2}
=-\frac{\sqrt{42}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*-1}=\frac{0+2\sqrt{42}}{-2}
=\frac{2\sqrt{42}}{-2}
=\frac{\sqrt{42}}{-1}
$