F(x)=(9x-1)(7x-3)

Solution for F(x)=(9x-1)(7x-3) equation:

(F)=(9F-1)(7F-3)

We move all terms to the left:

(F)-((9F-1)(7F-3))=0

We multiply parentheses ..

-((+63F^2-27F-7F+3))+F=0


We calculate terms in parentheses: -((+63F^2-27F-7F+3)), so:

(+63F^2-27F-7F+3)

We get rid of parentheses

63F^2-27F-7F+3

We add all the numbers together, and all the variables

63F^2-34F+3

Back to the equation:

-(63F^2-34F+3)


We add all the numbers together, and all the variables

F-(63F^2-34F+3)=0

We get rid of parentheses

-63F^2+F+34F-3=0

We add all the numbers together, and all the variables

-63F^2+35F-3=0

a = -63; b = 35; c = -3;
Δ = b2-4ac
Δ = 352-4·(-63)·(-3)
Δ = 469
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{469}}{2*-63}=\frac{-35-\sqrt{469}}{-126}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{469}}{2*-63}=\frac{-35+\sqrt{469}}{-126}
$