4a^2-16=2a+4a+8a+16

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

4a^2-16=2a+4a+8a+16

We move all terms to the left:

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

We add all the numbers together, and all the variables

4a^2-(14a+16)-16=0

We get rid of parentheses

4a^2-14a-16-16=0

We add all the numbers together, and all the variables

4a^2-14a-32=0

a = 4; b = -14; c = -32;
Δ = b2-4ac
Δ = -142-4·4·(-32)
Δ = 708
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:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{177}}{2*4}=\frac{14-2\sqrt{177}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{177}}{2*4}=\frac{14+2\sqrt{177}}{8}
$