5n-(20+n)n=1.5

Solution for 5n-(20+n)n=1.5 equation:

5n-(20+n)n=1.5

We move all terms to the left:

5n-(20+n)n-(1.5)=0

We add all the numbers together, and all the variables

5n-(n+20)n-(1.5)=0

We add all the numbers together, and all the variables

5n-(n+20)n-1.5=0

We multiply parentheses

-n^2+5n-20n-1.5=0

We add all the numbers together, and all the variables

-1n^2-15n-1.5=0

a = -1; b = -15; c = -1.5;
Δ = b2-4ac
Δ = -152-4·(-1)·(-1.5)
Δ = 219
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{-(-15)-\sqrt{219}}{2*-1}=\frac{15-\sqrt{219}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{219}}{2*-1}=\frac{15+\sqrt{219}}{-2}
$