r(r+2)-224=0

Solution for r(r+2)-224=0 equation:

r(r+2)-224=0

We multiply parentheses

r^2+2r-224=0

a = 1; b = 2; c = -224;
Δ = b2-4ac
Δ = 22-4·1·(-224)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-30}{2*1}=\frac{-32}{2}
=-16
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+30}{2*1}=\frac{28}{2}
=14
$