r(r+2)-143=0

Solution for r(r+2)-143=0 equation:

r(r+2)-143=0

We multiply parentheses

r^2+2r-143=0

a = 1; b = 2; c = -143;
Δ = b2-4ac
Δ = 22-4·1·(-143)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-24}{2*1}=\frac{-26}{2}
=-13
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+24}{2*1}=\frac{22}{2}
=11
$