4a^2-12a+16-327=0

Solution for 4a^2-12a+16-327=0 equation:

4a^2-12a+16-327=0

We add all the numbers together, and all the variables

4a^2-12a-311=0

a = 4; b = -12; c = -311;
Δ = b2-4ac
Δ = -122-4·4·(-311)
Δ = 5120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5120}=\sqrt{1024*5}=\sqrt{1024}*\sqrt{5}=32\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-32\sqrt{5}}{2*4}=\frac{12-32\sqrt{5}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+32\sqrt{5}}{2*4}=\frac{12+32\sqrt{5}}{8}
$