5n(n-2)=45

Solution for 5n(n-2)=45 equation:

5n(n-2)=45

We move all terms to the left:

5n(n-2)-(45)=0

We multiply parentheses

5n^2-10n-45=0

a = 5; b = -10; c = -45;
Δ = b2-4ac
Δ = -102-4·5·(-45)
Δ = 1000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{10}}{2*5}=\frac{10-10\sqrt{10}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{10}}{2*5}=\frac{10+10\sqrt{10}}{10}
$