X^2+147=(2x)^2

Solution for X^2+147=(2x)^2 equation:

X^2+147=(2X)^2

We move all terms to the left:

X^2+147-((2X)^2)=0

determiningTheFunctionDomain
X^2-2X^2+147=0

We add all the numbers together, and all the variables

-1X^2+147=0

a = -1; b = 0; c = +147;
Δ = b2-4ac
Δ = 02-4·(-1)·147
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{3}}{2*-1}=\frac{0-14\sqrt{3}}{-2}
=-\frac{14\sqrt{3}}{-2}
=-\frac{7\sqrt{3}}{-1}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{3}}{2*-1}=\frac{0+14\sqrt{3}}{-2}
=\frac{14\sqrt{3}}{-2}
=\frac{7\sqrt{3}}{-1}
$