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

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

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

We move all terms to the left:

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


Domain of the equation: 2F+7)!=0

F∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2F^2-18F^2-14F+9=0

We add all the numbers together, and all the variables

-16F^2-14F+9=0

a = -16; b = -14; c = +9;
Δ = b2-4ac
Δ = -142-4·(-16)·9
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{193}}{2*-16}=\frac{14-2\sqrt{193}}{-32}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{193}}{2*-16}=\frac{14+2\sqrt{193}}{-32}
$