120=7n+n2

Solution for 120=7n+n2 equation:

120=7n+n2

We move all terms to the left:

120-(7n+n2)=0

We add all the numbers together, and all the variables

-(+7n+n^2)+120=0

We get rid of parentheses

-n^2-7n+120=0

We add all the numbers together, and all the variables

-1n^2-7n+120=0

a = -1; b = -7; c = +120;
Δ = b2-4ac
Δ = -72-4·(-1)·120
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-23}{2*-1}=\frac{-16}{-2}
=+8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*-1}=\frac{30}{-2}
=-15
$