116+20r=2r^2

Solution for 116+20r=2r^2 equation:

116+20r=2r^2

We move all terms to the left:

116+20r-(2r^2)=0

determiningTheFunctionDomain
-2r^2+20r+116=0

a = -2; b = 20; c = +116;
Δ = b2-4ac
Δ = 202-4·(-2)·116
Δ = 1328
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:

$\sqrt{\Delta}=\sqrt{1328}=\sqrt{16*83}=\sqrt{16}*\sqrt{83}=4\sqrt{83}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{83}}{2*-2}=\frac{-20-4\sqrt{83}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{83}}{2*-2}=\frac{-20+4\sqrt{83}}{-4}
$