2(x+3)=(4x)2

Solution for 2(x+3)=(4x)2 equation:

2(x+3)=(4x)2

We move all terms to the left:

2(x+3)-((4x)2)=0

determiningTheFunctionDomain
2(x+3)-4x2=0

We add all the numbers together, and all the variables

-4x^2+2(x+3)=0

We multiply parentheses

-4x^2+2x+6=0

a = -4; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-4)·6
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*-4}=\frac{-12}{-8}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*-4}=\frac{8}{-8}
=-1
$