F(x)=x(9x-2)+4x-12

Solution for F(x)=x(9x-2)+4x-12 equation:

(F)=F(9F-2)+4F-12

We move all terms to the left:

(F)-(F(9F-2)+4F-12)=0


We calculate terms in parentheses: -(F(9F-2)+4F-12), so:

F(9F-2)+4F-12

We add all the numbers together, and all the variables

4F+F(9F-2)-12

We multiply parentheses

9F^2+4F-2F-12

We add all the numbers together, and all the variables

9F^2+2F-12

Back to the equation:

-(9F^2+2F-12)


We get rid of parentheses

-9F^2+F-2F+12=0

We add all the numbers together, and all the variables

-9F^2-1F+12=0

a = -9; b = -1; c = +12;
Δ = b2-4ac
Δ = -12-4·(-9)·12
Δ = 433
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{-(-1)-\sqrt{433}}{2*-9}=\frac{1-\sqrt{433}}{-18}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{433}}{2*-9}=\frac{1+\sqrt{433}}{-18}
$