x^2+x^2+8x+64=484

Solution for x^2+x^2+8x+64=484 equation:

x^2+x^2+8x+64=484

We move all terms to the left:

x^2+x^2+8x+64-(484)=0

We add all the numbers together, and all the variables

2x^2+8x-420=0

a = 2; b = 8; c = -420;
Δ = b2-4ac
Δ = 82-4·2·(-420)
Δ = 3424
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:

$\sqrt{\Delta}=\sqrt{3424}=\sqrt{16*214}=\sqrt{16}*\sqrt{214}=4\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{214}}{2*2}=\frac{-8-4\sqrt{214}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{214}}{2*2}=\frac{-8+4\sqrt{214}}{4}
$