F(x)=-3(x-10)(x-4)

Solution for F(x)=-3(x-10)(x-4) equation:

(F)=-3(F-10)(F-4)

We move all terms to the left:

(F)-(-3(F-10)(F-4))=0

We multiply parentheses ..

-(-3(+F^2-4F-10F+40))+F=0


We calculate terms in parentheses: -(-3(+F^2-4F-10F+40)), so:

-3(+F^2-4F-10F+40)

We multiply parentheses

-3F^2+12F+30F-120

We add all the numbers together, and all the variables

-3F^2+42F-120

Back to the equation:

-(-3F^2+42F-120)


We get rid of parentheses

3F^2-42F+F+120=0

We add all the numbers together, and all the variables

3F^2-41F+120=0

a = 3; b = -41; c = +120;
Δ = b2-4ac
Δ = -412-4·3·120
Δ = 241
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{-(-41)-\sqrt{241}}{2*3}=\frac{41-\sqrt{241}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{241}}{2*3}=\frac{41+\sqrt{241}}{6}
$