X^2+8x+16=12x^2

Solution for X^2+8x+16=12x^2 equation:

X^2+8X+16=12X^2

We move all terms to the left:

X^2+8X+16-(12X^2)=0

determiningTheFunctionDomain
X^2-12X^2+8X+16=0

We add all the numbers together, and all the variables

-11X^2+8X+16=0

a = -11; b = 8; c = +16;
Δ = b2-4ac
Δ = 82-4·(-11)·16
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{3}}{2*-11}=\frac{-8-16\sqrt{3}}{-22}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{3}}{2*-11}=\frac{-8+16\sqrt{3}}{-22}
$