x^2+75=(2x)^2

Solution for x^2+75=(2x)^2 equation:

x^2+75=(2x)^2

We move all terms to the left:

x^2+75-((2x)^2)=0

determiningTheFunctionDomain
x^2-2x^2+75=0

We add all the numbers together, and all the variables

-1x^2+75=0

a = -1; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-1)·75
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*-1}=\frac{0-10\sqrt{3}}{-2}
=-\frac{10\sqrt{3}}{-2}
=-\frac{5\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*-1}=\frac{0+10\sqrt{3}}{-2}
=\frac{10\sqrt{3}}{-2}
=\frac{5\sqrt{3}}{-1}
$