F(x)=(6x-9)(7x-6)

Solution for F(x)=(6x-9)(7x-6) equation:

(F)=(6F-9)(7F-6)

We move all terms to the left:

(F)-((6F-9)(7F-6))=0

We multiply parentheses ..

-((+42F^2-36F-63F+54))+F=0


We calculate terms in parentheses: -((+42F^2-36F-63F+54)), so:

(+42F^2-36F-63F+54)

We get rid of parentheses

42F^2-36F-63F+54

We add all the numbers together, and all the variables

42F^2-99F+54

Back to the equation:

-(42F^2-99F+54)


We add all the numbers together, and all the variables

F-(42F^2-99F+54)=0

We get rid of parentheses

-42F^2+F+99F-54=0

We add all the numbers together, and all the variables

-42F^2+100F-54=0

a = -42; b = 100; c = -54;
Δ = b2-4ac
Δ = 1002-4·(-42)·(-54)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{58}}{2*-42}=\frac{-100-4\sqrt{58}}{-84}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{58}}{2*-42}=\frac{-100+4\sqrt{58}}{-84}
$