5n(n-2)=5n-10

Solution for 5n(n-2)=5n-10 equation:

5n(n-2)=5n-10

We move all terms to the left:

5n(n-2)-(5n-10)=0

We multiply parentheses

5n^2-10n-(5n-10)=0

We get rid of parentheses

5n^2-10n-5n+10=0

We add all the numbers together, and all the variables

5n^2-15n+10=0

a = 5; b = -15; c = +10;
Δ = b2-4ac
Δ = -152-4·5·10
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5}{2*5}=\frac{10}{10}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5}{2*5}=\frac{20}{10}
=2
$