F(x)=(3x-2)(7-5x)

Solution for F(x)=(3x-2)(7-5x) equation:

(F)=(3F-2)(7-5F)

We move all terms to the left:

(F)-((3F-2)(7-5F))=0

We add all the numbers together, and all the variables

F-((3F-2)(-5F+7))=0

We multiply parentheses ..

-((-15F^2+21F+10F-14))+F=0


We calculate terms in parentheses: -((-15F^2+21F+10F-14)), so:

(-15F^2+21F+10F-14)

We get rid of parentheses

-15F^2+21F+10F-14

We add all the numbers together, and all the variables

-15F^2+31F-14

Back to the equation:

-(-15F^2+31F-14)


We get rid of parentheses

15F^2-31F+F+14=0

We add all the numbers together, and all the variables

15F^2-30F+14=0

a = 15; b = -30; c = +14;
Δ = b2-4ac
Δ = -302-4·15·14
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{15}}{2*15}=\frac{30-2\sqrt{15}}{30}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{15}}{2*15}=\frac{30+2\sqrt{15}}{30}
$