3416.32=106.76r+6.28r^2

Solution for 3416.32=106.76r+6.28r^2 equation:

3416.32=106.76r+6.28r^2

We move all terms to the left:

3416.32-(106.76r+6.28r^2)=0

We get rid of parentheses

-6.28r^2-106.76r+3416.32=0

a = -6.28; b = -106.76; c = +3416.32;
Δ = b2-4ac
Δ = -106.762-4·(-6.28)·3416.32
Δ = 97215.656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106.76)-\sqrt{97215.656}}{2*-6.28}=\frac{106.76-\sqrt{97215.656}}{-12.56}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106.76)+\sqrt{97215.656}}{2*-6.28}=\frac{106.76+\sqrt{97215.656}}{-12.56}
$