-7n(-n-8)=105

Solution for -7n(-n-8)=105 equation:

-7n(-n-8)=105

We move all terms to the left:

-7n(-n-8)-(105)=0

We add all the numbers together, and all the variables

-7n(-1n-8)-105=0

We multiply parentheses

7n^2+56n-105=0

a = 7; b = 56; c = -105;
Δ = b2-4ac
Δ = 562-4·7·(-105)
Δ = 6076
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6076}=\sqrt{196*31}=\sqrt{196}*\sqrt{31}=14\sqrt{31}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-14\sqrt{31}}{2*7}=\frac{-56-14\sqrt{31}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+14\sqrt{31}}{2*7}=\frac{-56+14\sqrt{31}}{14}
$