n^2-5n-3=47

Solution for n^2-5n-3=47 equation:

n^2-5n-3=47

We move all terms to the left:

n^2-5n-3-(47)=0

We add all the numbers together, and all the variables

n^2-5n-50=0

a = 1; b = -5; c = -50;
Δ = b2-4ac
Δ = -52-4·1·(-50)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*1}=\frac{-10}{2}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*1}=\frac{20}{2}
=10
$