r^2-14r=14

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

r^2-14r=14

We move all terms to the left:

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

a = 1; b = -14; c = -14;
Δ = b2-4ac
Δ = -142-4·1·(-14)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{7}}{2*1}=\frac{14-6\sqrt{7}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{7}}{2*1}=\frac{14+6\sqrt{7}}{2}
$