r^2-14r=19

Solution for r^2-14r=19 equation:

r^2-14r=19

We move all terms to the left:

r^2-14r-(19)=0

a = 1; b = -14; c = -19;
Δ = b2-4ac
Δ = -142-4·1·(-19)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{17}}{2*1}=\frac{14-4\sqrt{17}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{17}}{2*1}=\frac{14+4\sqrt{17}}{2}
$