F(x)=5/x-14+10

Solution for F(x)=5/x-14+10 equation:

(F)=5/F-14+10

We move all terms to the left:

(F)-(5/F-14+10)=0


Domain of the equation: F-14+10)!=0

We move all terms containing F to the left, all other terms to the right

F+10)!=14

F∈R


We add all the numbers together, and all the variables

F-(5/F-4)=0

We get rid of parentheses

F-5/F+4=0

We multiply all the terms by the denominator


F*F+4*F-5=0

We add all the numbers together, and all the variables

4F+F*F-5=0

Wy multiply elements

F^2+4F-5=0

a = 1; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·1·(-5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6}{2*1}=\frac{-10}{2}
=-5
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6}{2*1}=\frac{2}{2}
=1
$