r^2-2r+32=83

Solution for r^2-2r+32=83 equation:

r^2-2r+32=83

We move all terms to the left:

r^2-2r+32-(83)=0

We add all the numbers together, and all the variables

r^2-2r-51=0

a = 1; b = -2; c = -51;
Δ = b2-4ac
Δ = -22-4·1·(-51)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{13}}{2*1}=\frac{2-4\sqrt{13}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{13}}{2*1}=\frac{2+4\sqrt{13}}{2}
$