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=0

a = 4; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·4·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*4}=\frac{0}{8}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*4}=\frac{28}{8}
=3+1/2
$