-5n^2+8n+73=4

Solution for -5n^2+8n+73=4 equation:

-5n^2+8n+73=4

We move all terms to the left:

-5n^2+8n+73-(4)=0

We add all the numbers together, and all the variables

-5n^2+8n+69=0

a = -5; b = 8; c = +69;
Δ = b2-4ac
Δ = 82-4·(-5)·69
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-38}{2*-5}=\frac{-46}{-10}
=4+3/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+38}{2*-5}=\frac{30}{-10}
=-3
$