(f-9)(6f-5)=0

Solution for (f-9)(6f-5)=0 equation:

(f-9)(6f-5)=0

We multiply parentheses ..

(+6f^2-5f-54f+45)=0

We get rid of parentheses

6f^2-5f-54f+45=0

We add all the numbers together, and all the variables

6f^2-59f+45=0

a = 6; b = -59; c = +45;
Δ = b2-4ac
Δ = -592-4·6·45
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-49}{2*6}=\frac{10}{12}
=5/6
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+49}{2*6}=\frac{108}{12}
=9
$