x^2-16x+13=29

Solution for x^2-16x+13=29 equation:

x^2-16x+13=29

We move all terms to the left:

x^2-16x+13-(29)=0

We add all the numbers together, and all the variables

x^2-16x-16=0

a = 1; b = -16; c = -16;
Δ = b2-4ac
Δ = -162-4·1·(-16)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{5}}{2*1}=\frac{16-8\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{5}}{2*1}=\frac{16+8\sqrt{5}}{2}
$