4a2-8a=16

Solution for 4a2-8a=16 equation:

4a^2-8a=16

We move all terms to the left:

4a^2-8a-(16)=0

a = 4; b = -8; c = -16;
Δ = b2-4ac
Δ = -82-4·4·(-16)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{5}}{2*4}=\frac{8-8\sqrt{5}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{5}}{2*4}=\frac{8+8\sqrt{5}}{8}
$