-7+(8n)(n+1)=n-7

Solution for -7+(8n)(n+1)=n-7 equation:

-7+(8n)(n+1)=n-7

We move all terms to the left:

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

We multiply parentheses

8n^2+8n-(n-7)-7=0

We get rid of parentheses

8n^2+8n-n+7-7=0

We add all the numbers together, and all the variables

8n^2+7n=0

a = 8; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·8·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*8}=\frac{-14}{16}
=-7/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*8}=\frac{0}{16}
=0
$