F(x)=(x-15)(x-22)

Solution for F(x)=(x-15)(x-22) equation:

(F)=(F-15)(F-22)

We move all terms to the left:

(F)-((F-15)(F-22))=0

We multiply parentheses ..

-((+F^2-22F-15F+330))+F=0


We calculate terms in parentheses: -((+F^2-22F-15F+330)), so:

(+F^2-22F-15F+330)

We get rid of parentheses

F^2-22F-15F+330

We add all the numbers together, and all the variables

F^2-37F+330

Back to the equation:

-(F^2-37F+330)


We add all the numbers together, and all the variables

F-(F^2-37F+330)=0

We get rid of parentheses

-F^2+F+37F-330=0

We add all the numbers together, and all the variables

-1F^2+38F-330=0

a = -1; b = 38; c = -330;
Δ = b2-4ac
Δ = 382-4·(-1)·(-330)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{31}}{2*-1}=\frac{-38-2\sqrt{31}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{31}}{2*-1}=\frac{-38+2\sqrt{31}}{-2}
$