0=n^2-7n-4

Solution for 0=n^2-7n-4 equation:

0=n^2-7n-4

We move all terms to the left:

0-(n^2-7n-4)=0

We add all the numbers together, and all the variables

-(n^2-7n-4)=0

We get rid of parentheses

-n^2+7n+4=0

We add all the numbers together, and all the variables

-1n^2+7n+4=0

a = -1; b = 7; c = +4;
Δ = b2-4ac
Δ = 72-4·(-1)·4
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{65}}{2*-1}=\frac{-7-\sqrt{65}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{65}}{2*-1}=\frac{-7+\sqrt{65}}{-2}
$