4x^2+8x+16=216

Solution for 4x^2+8x+16=216 equation:

4x^2+8x+16=216

We move all terms to the left:

4x^2+8x+16-(216)=0

We add all the numbers together, and all the variables

4x^2+8x-200=0

a = 4; b = 8; c = -200;
Δ = b2-4ac
Δ = 82-4·4·(-200)
Δ = 3264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{51}}{2*4}=\frac{-8-8\sqrt{51}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{51}}{2*4}=\frac{-8+8\sqrt{51}}{8}
$