(5n-6)(n-3)=0

Solution for (5n-6)(n-3)=0 equation:

(5n-6)(n-3)=0

We multiply parentheses ..

(+5n^2-15n-6n+18)=0

We get rid of parentheses

5n^2-15n-6n+18=0

We add all the numbers together, and all the variables

5n^2-21n+18=0

a = 5; b = -21; c = +18;
Δ = b2-4ac
Δ = -212-4·5·18
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9}{2*5}=\frac{12}{10}
=1+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9}{2*5}=\frac{30}{10}
=3
$