-6.5n(n-5)=18.2

Solution for -6.5n(n-5)=18.2 equation:

-6.5n(n-5)=18.2

We move all terms to the left:

-6.5n(n-5)-(18.2)=0

We add all the numbers together, and all the variables

-6.5n(n-5)-18.2=0

We multiply parentheses

-6n^2+30n-18.2=0

a = -6; b = 30; c = -18.2;
Δ = b2-4ac
Δ = 302-4·(-6)·(-18.2)
Δ = 463.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-\sqrt{463.2}}{2*-6}=\frac{-30-\sqrt{463.2}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+\sqrt{463.2}}{2*-6}=\frac{-30+\sqrt{463.2}}{-12}
$