(n-3)(5n-2)=0

Solution for (n-3)(5n-2)=0 equation:

(n-3)(5n-2)=0

We multiply parentheses ..

(+5n^2-2n-15n+6)=0

We get rid of parentheses

5n^2-2n-15n+6=0

We add all the numbers together, and all the variables

5n^2-17n+6=0

a = 5; b = -17; c = +6;
Δ = b2-4ac
Δ = -172-4·5·6
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-13}{2*5}=\frac{4}{10}
=2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+13}{2*5}=\frac{30}{10}
=3
$