0=n^2+47n-72

Solution for 0=n^2+47n-72 equation:

0=n^2+47n-72

We move all terms to the left:

0-(n^2+47n-72)=0

We add all the numbers together, and all the variables

-(n^2+47n-72)=0

We get rid of parentheses

-n^2-47n+72=0

We add all the numbers together, and all the variables

-1n^2-47n+72=0

a = -1; b = -47; c = +72;
Δ = b2-4ac
Δ = -472-4·(-1)·72
Δ = 2497
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{-(-47)-\sqrt{2497}}{2*-1}=\frac{47-\sqrt{2497}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2497}}{2*-1}=\frac{47+\sqrt{2497}}{-2}
$