F(x)=-2x-7/2x-9

Solution for F(x)=-2x-7/2x-9 equation:

(F)=-2F-7/2F-9

We move all terms to the left:

(F)-(-2F-7/2F-9)=0


Domain of the equation: 2F-9)!=0

F∈R


We get rid of parentheses

F+2F+7/2F+9=0

We multiply all the terms by the denominator


F*2F+2F*2F+9*2F+7=0

Wy multiply elements

2F^2+4F^2+18F+7=0

We add all the numbers together, and all the variables

6F^2+18F+7=0

a = 6; b = 18; c = +7;
Δ = b2-4ac
Δ = 182-4·6·7
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{39}}{2*6}=\frac{-18-2\sqrt{39}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{39}}{2*6}=\frac{-18+2\sqrt{39}}{12}
$