F(x)=0.25(x-1)(x-12)

Solution for F(x)=0.25(x-1)(x-12) equation:

(F)=0.25(F-1)(F-12)

We move all terms to the left:

(F)-(0.25(F-1)(F-12))=0

We multiply parentheses ..

-(0.25(+F^2-12F-1F+12))+F=0


We calculate terms in parentheses: -(0.25(+F^2-12F-1F+12)), so:

0.25(+F^2-12F-1F+12)

We multiply parentheses

0.25F^2-3F-0.25F+3

We add all the numbers together, and all the variables

0.25F^2-3.25F+3

Back to the equation:

-(0.25F^2-3.25F+3)


We add all the numbers together, and all the variables

F-(0.25F^2-3.25F+3)=0

We get rid of parentheses

-0.25F^2+F+3.25F-3=0

We add all the numbers together, and all the variables

-0.25F^2+4.25F-3=0

a = -0.25; b = 4.25; c = -3;
Δ = b2-4ac
Δ = 4.252-4·(-0.25)·(-3)
Δ = 15.0625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4.25)-\sqrt{15.0625}}{2*-0.25}=\frac{-4.25-\sqrt{15.0625}}{-0.5}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.25)+\sqrt{15.0625}}{2*-0.25}=\frac{-4.25+\sqrt{15.0625}}{-0.5}
$