-5n+5n(n-7)=-40+5n

Solution for -5n+5n(n-7)=-40+5n equation:

-5n+5n(n-7)=-40+5n

We move all terms to the left:

-5n+5n(n-7)-(-40+5n)=0

We add all the numbers together, and all the variables

-5n+5n(n-7)-(5n-40)=0

We multiply parentheses

5n^2-5n-35n-(5n-40)=0

We get rid of parentheses

5n^2-5n-35n-5n+40=0

We add all the numbers together, and all the variables

5n^2-45n+40=0

a = 5; b = -45; c = +40;
Δ = b2-4ac
Δ = -452-4·5·40
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-35}{2*5}=\frac{10}{10}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+35}{2*5}=\frac{80}{10}
=8
$