F(x)=3x(x-7)-2(x-4)

Solution for F(x)=3x(x-7)-2(x-4) equation:

(F)=3F(F-7)-2(F-4)

We move all terms to the left:

(F)-(3F(F-7)-2(F-4))=0


We calculate terms in parentheses: -(3F(F-7)-2(F-4)), so:

3F(F-7)-2(F-4)

We multiply parentheses

3F^2-21F-2F+8

We add all the numbers together, and all the variables

3F^2-23F+8

Back to the equation:

-(3F^2-23F+8)


We get rid of parentheses

-3F^2+F+23F-8=0

We add all the numbers together, and all the variables

-3F^2+24F-8=0

a = -3; b = 24; c = -8;
Δ = b2-4ac
Δ = 242-4·(-3)·(-8)
Δ = 480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{30}}{2*-3}=\frac{-24-4\sqrt{30}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{30}}{2*-3}=\frac{-24+4\sqrt{30}}{-6}
$