4a^2-12a-20a+16-327=0

Solution for 4a^2-12a-20a+16-327=0 equation:

4a^2-12a-20a+16-327=0

We add all the numbers together, and all the variables

4a^2-32a-311=0

a = 4; b = -32; c = -311;
Δ = b2-4ac
Δ = -322-4·4·(-311)
Δ = 6000
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:

$\sqrt{\Delta}=\sqrt{6000}=\sqrt{400*15}=\sqrt{400}*\sqrt{15}=20\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-20\sqrt{15}}{2*4}=\frac{32-20\sqrt{15}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+20\sqrt{15}}{2*4}=\frac{32+20\sqrt{15}}{8}
$