r2+14r=39

Solution for r2+14r=39 equation:

r2+14r=39

We move all terms to the left:

r2+14r-(39)=0

We add all the numbers together, and all the variables

r^2+14r-39=0

a = 1; b = 14; c = -39;
Δ = b2-4ac
Δ = 142-4·1·(-39)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{22}}{2*1}=\frac{-14-4\sqrt{22}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{22}}{2*1}=\frac{-14+4\sqrt{22}}{2}
$