F(n)=3n2+80*2n

Solution for F(n)=3n2+80*2n equation:

(F)=3F^2+80*2F

We move all terms to the left:

(F)-(3F^2+80*2F)=0

We get rid of parentheses

-3F^2+F-80*2F=0

Wy multiply elements

-3F^2+F-160F=0

We add all the numbers together, and all the variables

-3F^2-159F=0

a = -3; b = -159; c = 0;
Δ = b2-4ac
Δ = -1592-4·(-3)·0
Δ = 25281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25281}=159$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-159)-159}{2*-3}=\frac{0}{-6}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-159)+159}{2*-3}=\frac{318}{-6}
=-53
$