(2n-5)(n-6)=0

Solution for (2n-5)(n-6)=0 equation:

(2n-5)(n-6)=0

We multiply parentheses ..

(+2n^2-12n-5n+30)=0

We get rid of parentheses

2n^2-12n-5n+30=0

We add all the numbers together, and all the variables

2n^2-17n+30=0

a = 2; b = -17; c = +30;
Δ = b2-4ac
Δ = -172-4·2·30
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-7}{2*2}=\frac{10}{4}
=2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+7}{2*2}=\frac{24}{4}
=6
$