4x^2-16x+16=48

Solution for 4x^2-16x+16=48 equation:

4x^2-16x+16=48

We move all terms to the left:

4x^2-16x+16-(48)=0

We add all the numbers together, and all the variables

4x^2-16x-32=0

a = 4; b = -16; c = -32;
Δ = b2-4ac
Δ = -162-4·4·(-32)
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{-(-16)-16\sqrt{3}}{2*4}=\frac{16-16\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{3}}{2*4}=\frac{16+16\sqrt{3}}{8}
$