(x+4)2=4x2

Solution for (x+4)2=4x2 equation:

(x+4)2=4x^2

We move all terms to the left:

(x+4)2-(4x^2)=0

determiningTheFunctionDomain
-4x^2+(x+4)2=0

We multiply parentheses

-4x^2+2x+8=0

a = -4; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-4)·8
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{33}}{2*-4}=\frac{-2-2\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{33}}{2*-4}=\frac{-2+2\sqrt{33}}{-8}
$