4a^2-8a+16=24

Solution for 4a^2-8a+16=24 equation:

4a^2-8a+16=24

We move all terms to the left:

4a^2-8a+16-(24)=0

We add all the numbers together, and all the variables

4a^2-8a-8=0

a = 4; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·4·(-8)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{3}}{2*4}=\frac{8-8\sqrt{3}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{3}}{2*4}=\frac{8+8\sqrt{3}}{8}
$