4a^2-56a+16=0

Solution for 4a^2-56a+16=0 equation:

4a^2-56a+16=0

a = 4; b = -56; c = +16;
Δ = b2-4ac
Δ = -562-4·4·16
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-24\sqrt{5}}{2*4}=\frac{56-24\sqrt{5}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+24\sqrt{5}}{2*4}=\frac{56+24\sqrt{5}}{8}
$