r(r+1)=210

Solution for r(r+1)=210 equation:

r(r+1)=210

We move all terms to the left:

r(r+1)-(210)=0

We multiply parentheses

r^2+r-210=0

a = 1; b = 1; c = -210;
Δ = b2-4ac
Δ = 12-4·1·(-210)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-29}{2*1}=\frac{-30}{2}
=-15
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+29}{2*1}=\frac{28}{2}
=14
$