0.114856=2r^2-19r

Solution for 0.114856=2r^2-19r equation:

0.114856=2r^2-19r

We move all terms to the left:

0.114856-(2r^2-19r)=0

We get rid of parentheses

-2r^2+19r+0.114856=0

a = -2; b = 19; c = +0.114856;
Δ = b2-4ac
Δ = 192-4·(-2)·0.114856
Δ = 361.918848
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{-(19)-\sqrt{361.918848}}{2*-2}=\frac{-19-\sqrt{361.918848}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{361.918848}}{2*-2}=\frac{-19+\sqrt{361.918848}}{-4}
$