F(x)=(5x+7)(4-3x)

Solution for F(x)=(5x+7)(4-3x) equation:

(F)=(5F+7)(4-3F)

We move all terms to the left:

(F)-((5F+7)(4-3F))=0

We add all the numbers together, and all the variables

F-((5F+7)(-3F+4))=0

We multiply parentheses ..

-((-15F^2+20F-21F+28))+F=0


We calculate terms in parentheses: -((-15F^2+20F-21F+28)), so:

(-15F^2+20F-21F+28)

We get rid of parentheses

-15F^2+20F-21F+28

We add all the numbers together, and all the variables

-15F^2-1F+28

Back to the equation:

-(-15F^2-1F+28)


We get rid of parentheses

15F^2+1F+F-28=0

We add all the numbers together, and all the variables

15F^2+2F-28=0

a = 15; b = 2; c = -28;
Δ = b2-4ac
Δ = 22-4·15·(-28)
Δ = 1684
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:

$\sqrt{\Delta}=\sqrt{1684}=\sqrt{4*421}=\sqrt{4}*\sqrt{421}=2\sqrt{421}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{421}}{2*15}=\frac{-2-2\sqrt{421}}{30}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{421}}{2*15}=\frac{-2+2\sqrt{421}}{30}
$