0=(n^2)+n-144

Solution for 0=(n^2)+n-144 equation:

0=(n^2)+n-144

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-n^2-n+144=0

We add all the numbers together, and all the variables

-1n^2-1n+144=0

a = -1; b = -1; c = +144;
Δ = b2-4ac
Δ = -12-4·(-1)·144
Δ = 577
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{577}}{2*-1}=\frac{1-\sqrt{577}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{577}}{2*-1}=\frac{1+\sqrt{577}}{-2}
$