n^2-7n-5=3

Solution for n^2-7n-5=3 equation:

n^2-7n-5=3

We move all terms to the left:

n^2-7n-5-(3)=0

We add all the numbers together, and all the variables

n^2-7n-8=0

a = 1; b = -7; c = -8;
Δ = b2-4ac
Δ = -72-4·1·(-8)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*1}=\frac{-2}{2}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*1}=\frac{16}{2}
=8
$