F(-1)=2x+5/8x-9

Solution for F(-1)=2x+5/8x-9 equation:

(-1)=2F+5/8F-9

We move all terms to the left:

(-1)-(2F+5/8F-9)=0


Domain of the equation: 8F-9)!=0

F∈R


We add all the numbers together, and all the variables

-(2F+5/8F-9)-1=0

We get rid of parentheses

-2F-5/8F+9-1=0

We multiply all the terms by the denominator


-2F*8F+9*8F-1*8F-5=0

Wy multiply elements

-16F^2+72F-8F-5=0

We add all the numbers together, and all the variables

-16F^2+64F-5=0

a = -16; b = 64; c = -5;
Δ = b2-4ac
Δ = 642-4·(-16)·(-5)
Δ = 3776
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:

$\sqrt{\Delta}=\sqrt{3776}=\sqrt{64*59}=\sqrt{64}*\sqrt{59}=8\sqrt{59}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{59}}{2*-16}=\frac{-64-8\sqrt{59}}{-32}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{59}}{2*-16}=\frac{-64+8\sqrt{59}}{-32}
$