F(x)=5x-7/6x-9

Solution for F(x)=5x-7/6x-9 equation:

(F)=5F-7/6F-9

We move all terms to the left:

(F)-(5F-7/6F-9)=0


Domain of the equation: 6F-9)!=0

F∈R


We get rid of parentheses

F-5F+7/6F+9=0

We multiply all the terms by the denominator


F*6F-5F*6F+9*6F+7=0

Wy multiply elements

6F^2-30F^2+54F+7=0

We add all the numbers together, and all the variables

-24F^2+54F+7=0

a = -24; b = 54; c = +7;
Δ = b2-4ac
Δ = 542-4·(-24)·7
Δ = 3588
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:

$\sqrt{\Delta}=\sqrt{3588}=\sqrt{4*897}=\sqrt{4}*\sqrt{897}=2\sqrt{897}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{897}}{2*-24}=\frac{-54-2\sqrt{897}}{-48}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{897}}{2*-24}=\frac{-54+2\sqrt{897}}{-48}
$