16r^2-8r+1=5

Solution for 16r^2-8r+1=5 equation:

16r^2-8r+1=5

We move all terms to the left:

16r^2-8r+1-(5)=0

We add all the numbers together, and all the variables

16r^2-8r-4=0

a = 16; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·16·(-4)
Δ = 320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{5}}{2*16}=\frac{8-8\sqrt{5}}{32}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{5}}{2*16}=\frac{8+8\sqrt{5}}{32}
$