2n(n+1)=144

Solution for 2n(n+1)=144 equation:

2n(n+1)=144

We move all terms to the left:

2n(n+1)-(144)=0

We multiply parentheses

2n^2+2n-144=0

a = 2; b = 2; c = -144;
Δ = b2-4ac
Δ = 22-4·2·(-144)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-34}{2*2}=\frac{-36}{4}
=-9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+34}{2*2}=\frac{32}{4}
=8
$