u^2+8u+16+2=29

Solution for u^2+8u+16+2=29 equation:

u^2+8u+16+2=29

We move all terms to the left:

u^2+8u+16+2-(29)=0

We add all the numbers together, and all the variables

u^2+8u-11=0

a = 1; b = 8; c = -11;
Δ = b2-4ac
Δ = 82-4·1·(-11)
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{3}}{2*1}=\frac{-8-6\sqrt{3}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{3}}{2*1}=\frac{-8+6\sqrt{3}}{2}
$