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

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

(F)=7F(F-3)

We move all terms to the left:

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


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

7F(F-3)

We multiply parentheses

7F^2-21F

Back to the equation:

-(7F^2-21F)


We get rid of parentheses

-7F^2+F+21F=0

We add all the numbers together, and all the variables

-7F^2+22F=0

a = -7; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-7)·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*-7}=\frac{-44}{-14}
=3+1/7
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-7}=\frac{0}{-14}
=0
$