x^2+6x+9=4x^2+4x+1

Solution for x^2+6x+9=4x^2+4x+1 equation:

x^2+6x+9=4x^2+4x+1

We move all terms to the left:

x^2+6x+9-(4x^2+4x+1)=0

We get rid of parentheses

x^2-4x^2+6x-4x-1+9=0

We add all the numbers together, and all the variables

-3x^2+2x+8=0

a = -3; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-3)·8
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*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*-3}=\frac{8}{-6}
=-1+1/3
$