712=8(n2-200)

Solution for 712=8(n2-200) equation:

712=8(n2-200)

We move all terms to the left:

712-(8(n2-200))=0

We add all the numbers together, and all the variables

-(8(+n^2-200))+712=0


We calculate terms in parentheses: -(8(+n^2-200)), so:

8(+n^2-200)

We multiply parentheses

8n^2-1600

Back to the equation:

-(8n^2-1600)


We get rid of parentheses

-8n^2+1600+712=0

We add all the numbers together, and all the variables

-8n^2+2312=0

a = -8; b = 0; c = +2312;
Δ = b2-4ac
Δ = 02-4·(-8)·2312
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-272}{2*-8}=\frac{-272}{-16}
=+17
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+272}{2*-8}=\frac{272}{-16}
=-17
$