r=14-2r^2

Solution for r=14-2r^2 equation:

r=14-2r^2

We move all terms to the left:

r-(14-2r^2)=0

We get rid of parentheses

2r^2+r-14=0

a = 2; b = 1; c = -14;
Δ = b2-4ac
Δ = 12-4·2·(-14)
Δ = 113
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{-(1)-\sqrt{113}}{2*2}=\frac{-1-\sqrt{113}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{113}}{2*2}=\frac{-1+\sqrt{113}}{4}
$