F(x)=0.75(x-1)(x-2)

Solution for F(x)=0.75(x-1)(x-2) equation:

(F)=0.75(F-1)(F-2)

We move all terms to the left:

(F)-(0.75(F-1)(F-2))=0

We multiply parentheses ..

-(0.75(+F^2-2F-1F+2))+F=0


We calculate terms in parentheses: -(0.75(+F^2-2F-1F+2)), so:

0.75(+F^2-2F-1F+2)

We multiply parentheses

0.75F^2-1.5F-0.75F+1.5

We add all the numbers together, and all the variables

0.75F^2-2.25F+1.5

Back to the equation:

-(0.75F^2-2.25F+1.5)


We add all the numbers together, and all the variables

F-(0.75F^2-2.25F+1.5)=0

We get rid of parentheses

-0.75F^2+F+2.25F-1.5=0

We add all the numbers together, and all the variables

-0.75F^2+3.25F-1.5=0

a = -0.75; b = 3.25; c = -1.5;
Δ = b2-4ac
Δ = 3.252-4·(-0.75)·(-1.5)
Δ = 6.0625
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{-(3.25)-\sqrt{6.0625}}{2*-0.75}=\frac{-3.25-\sqrt{6.0625}}{-1.5}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.25)+\sqrt{6.0625}}{2*-0.75}=\frac{-3.25+\sqrt{6.0625}}{-1.5}
$