3n-8n(n=99)

Solution for 3n-8n(n=99) equation:

3n-8n(n=99)

We move all terms to the left:

3n-8n(n-(99))=0

We multiply parentheses

-8n^2+3n+792n=0

We add all the numbers together, and all the variables

-8n^2+795n=0

a = -8; b = 795; c = 0;
Δ = b2-4ac
Δ = 7952-4·(-8)·0
Δ = 632025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{632025}=795$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(795)-795}{2*-8}=\frac{-1590}{-16}
=99+3/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(795)+795}{2*-8}=\frac{0}{-16}
=0
$