F(x)=(6x-1)(9x-4)

Solution for F(x)=(6x-1)(9x-4) equation:

(F)=(6F-1)(9F-4)

We move all terms to the left:

(F)-((6F-1)(9F-4))=0

We multiply parentheses ..

-((+54F^2-24F-9F+4))+F=0


We calculate terms in parentheses: -((+54F^2-24F-9F+4)), so:

(+54F^2-24F-9F+4)

We get rid of parentheses

54F^2-24F-9F+4

We add all the numbers together, and all the variables

54F^2-33F+4

Back to the equation:

-(54F^2-33F+4)


We add all the numbers together, and all the variables

F-(54F^2-33F+4)=0

We get rid of parentheses

-54F^2+F+33F-4=0

We add all the numbers together, and all the variables

-54F^2+34F-4=0

a = -54; b = 34; c = -4;
Δ = b2-4ac
Δ = 342-4·(-54)·(-4)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{73}}{2*-54}=\frac{-34-2\sqrt{73}}{-108}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{73}}{2*-54}=\frac{-34+2\sqrt{73}}{-108}
$