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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5n^2-40n+35=0

a = 5; b = -40; c = +35;
Δ = b2-4ac
Δ = -402-4·5·35
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-30}{2*5}=\frac{10}{10}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+30}{2*5}=\frac{70}{10}
=7
$