(x2-4x+3)2-4x2-9=16x

Solution for (x2-4x+3)2-4x2-9=16x equation:

(x2-4x+3)2-4x^2-9=16x

We move all terms to the left:

(x2-4x+3)2-4x^2-9-(16x)=0

We add all the numbers together, and all the variables

-4x^2+(+x^2-4x+3)2-16x-9=0

We multiply parentheses

-4x^2+2x^2-8x-16x+6-9=0

We add all the numbers together, and all the variables

-2x^2-24x-3=0

a = -2; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·(-2)·(-3)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{138}}{2*-2}=\frac{24-2\sqrt{138}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{138}}{2*-2}=\frac{24+2\sqrt{138}}{-4}
$