F(x)=-9x-6+x(2x-5)

Solution for F(x)=-9x-6+x(2x-5) equation:

(F)=-9F-6+F(2F-5)

We move all terms to the left:

(F)-(-9F-6+F(2F-5))=0


We calculate terms in parentheses: -(-9F-6+F(2F-5)), so:

-9F-6+F(2F-5)

determiningTheFunctionDomain
-9F+F(2F-5)-6

We multiply parentheses

2F^2-9F-5F-6

We add all the numbers together, and all the variables

2F^2-14F-6

Back to the equation:

-(2F^2-14F-6)


We get rid of parentheses

-2F^2+F+14F+6=0

We add all the numbers together, and all the variables

-2F^2+15F+6=0

a = -2; b = 15; c = +6;
Δ = b2-4ac
Δ = 152-4·(-2)·6
Δ = 273
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{-(15)-\sqrt{273}}{2*-2}=\frac{-15-\sqrt{273}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{273}}{2*-2}=\frac{-15+\sqrt{273}}{-4}
$