(x2+4x-4)2-9x2-36x+44=0

Solution for (x2+4x-4)2-9x2-36x+44=0 equation:

(x2+4x-4)2-9x^2-36x+44=0

We add all the numbers together, and all the variables

-9x^2+(+x^2+4x-4)2-36x+44=0

We multiply parentheses

-9x^2+2x^2+8x-36x-8+44=0

We add all the numbers together, and all the variables

-7x^2-28x+36=0

a = -7; b = -28; c = +36;
Δ = b2-4ac
Δ = -282-4·(-7)·36
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-16\sqrt{7}}{2*-7}=\frac{28-16\sqrt{7}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+16\sqrt{7}}{2*-7}=\frac{28+16\sqrt{7}}{-14}
$