F(x)=15/x-8

Solution for F(x)=15/x-8 equation:

(F)=15/F-8

We move all terms to the left:

(F)-(15/F-8)=0


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

F∈R


We get rid of parentheses

F-15/F+8=0

We multiply all the terms by the denominator


F*F+8*F-15=0

We add all the numbers together, and all the variables

8F+F*F-15=0

Wy multiply elements

F^2+8F-15=0

a = 1; b = 8; c = -15;
Δ = b2-4ac
Δ = 82-4·1·(-15)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{31}}{2*1}=\frac{-8-2\sqrt{31}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{31}}{2*1}=\frac{-8+2\sqrt{31}}{2}
$