r(r+6)=280

Solution for r(r+6)=280 equation:

r(r+6)=280

We move all terms to the left:

r(r+6)-(280)=0

We multiply parentheses

r^2+6r-280=0

a = 1; b = 6; c = -280;
Δ = b2-4ac
Δ = 62-4·1·(-280)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-34}{2*1}=\frac{-40}{2}
=-20
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+34}{2*1}=\frac{28}{2}
=14
$