X^2+x^2+4x+4+x^2+8x+16=80

Solution for X^2+x^2+4x+4+x^2+8x+16=80 equation:

X^2+X^2+4X+4+X^2+8X+16=80

We move all terms to the left:

X^2+X^2+4X+4+X^2+8X+16-(80)=0

We add all the numbers together, and all the variables

3X^2+12X-60=0

a = 3; b = 12; c = -60;
Δ = b2-4ac
Δ = 122-4·3·(-60)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{6}}{2*3}=\frac{-12-12\sqrt{6}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{6}}{2*3}=\frac{-12+12\sqrt{6}}{6}
$