F(x)=3x(4x-7)

Solution for F(x)=3x(4x-7) equation:

(F)=3F(4F-7)

We move all terms to the left:

(F)-(3F(4F-7))=0


We calculate terms in parentheses: -(3F(4F-7)), so:

3F(4F-7)

We multiply parentheses

12F^2-21F

Back to the equation:

-(12F^2-21F)


We get rid of parentheses

-12F^2+F+21F=0

We add all the numbers together, and all the variables

-12F^2+22F=0

a = -12; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-12)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-12}=\frac{-44}{-24}
=1+5/6
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-12}=\frac{0}{-24}
=0
$