r(r-14)=49

Solution for r(r-14)=49 equation:

r(r-14)=49

We move all terms to the left:

r(r-14)-(49)=0

We multiply parentheses

r^2-14r-49=0

a = 1; b = -14; c = -49;
Δ = b2-4ac
Δ = -142-4·1·(-49)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14\sqrt{2}}{2*1}=\frac{14-14\sqrt{2}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14\sqrt{2}}{2*1}=\frac{14+14\sqrt{2}}{2}
$