-n^2+6n=7

Solution for -n^2+6n=7 equation:

-n^2+6n=7

We move all terms to the left:

-n^2+6n-(7)=0

We add all the numbers together, and all the variables

-1n^2+6n-7=0

a = -1; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·(-1)·(-7)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{2}}{2*-1}=\frac{-6-2\sqrt{2}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{2}}{2*-1}=\frac{-6+2\sqrt{2}}{-2}
$