(n-8)(6n-5)=0

Solution for (n-8)(6n-5)=0 equation:

(n-8)(6n-5)=0

We multiply parentheses ..

(+6n^2-5n-48n+40)=0

We get rid of parentheses

6n^2-5n-48n+40=0

We add all the numbers together, and all the variables

6n^2-53n+40=0

a = 6; b = -53; c = +40;
Δ = b2-4ac
Δ = -532-4·6·40
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-43}{2*6}=\frac{10}{12}
=5/6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+43}{2*6}=\frac{96}{12}
=8
$