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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+3F^2-1F-21F+7))+F=0


We calculate terms in parentheses: -((+3F^2-1F-21F+7)), so:

(+3F^2-1F-21F+7)

We get rid of parentheses

3F^2-1F-21F+7

We add all the numbers together, and all the variables

3F^2-22F+7

Back to the equation:

-(3F^2-22F+7)


We add all the numbers together, and all the variables

F-(3F^2-22F+7)=0

We get rid of parentheses

-3F^2+F+22F-7=0

We add all the numbers together, and all the variables

-3F^2+23F-7=0

a = -3; b = 23; c = -7;
Δ = b2-4ac
Δ = 232-4·(-3)·(-7)
Δ = 445
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{-(23)-\sqrt{445}}{2*-3}=\frac{-23-\sqrt{445}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{445}}{2*-3}=\frac{-23+\sqrt{445}}{-6}
$