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

Solution for (n-2)(5n+2)=0 equation:

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

We multiply parentheses ..

(+5n^2+2n-10n-4)=0

We get rid of parentheses

5n^2+2n-10n-4=0

We add all the numbers together, and all the variables

5n^2-8n-4=0

a = 5; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·5·(-4)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*5}=\frac{-4}{10}
=-2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*5}=\frac{20}{10}
=2
$