(f-8)(6f+5)=0

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

(f-8)(6f+5)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6f^2-43f-40=0

a = 6; b = -43; c = -40;
Δ = b2-4ac
Δ = -432-4·6·(-40)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-53}{2*6}=\frac{-10}{12}
=-5/6
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+53}{2*6}=\frac{96}{12}
=8
$