147=14r+2r^2

Solution for 147=14r+2r^2 equation:

147=14r+2r^2

We move all terms to the left:

147-(14r+2r^2)=0

We get rid of parentheses

-2r^2-14r+147=0

a = -2; b = -14; c = +147;
Δ = b2-4ac
Δ = -142-4·(-2)·147
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14\sqrt{7}}{2*-2}=\frac{14-14\sqrt{7}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14\sqrt{7}}{2*-2}=\frac{14+14\sqrt{7}}{-4}
$