F(x)=144/x+7

Solution for F(x)=144/x+7 equation:

(F)=144/F+7

We move all terms to the left:

(F)-(144/F+7)=0


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

F∈R


We get rid of parentheses

F-144/F-7=0

We multiply all the terms by the denominator


F*F-7*F-144=0

We add all the numbers together, and all the variables

-7F+F*F-144=0

Wy multiply elements

F^2-7F-144=0

a = 1; b = -7; c = -144;
Δ = b2-4ac
Δ = -72-4·1·(-144)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-25}{2*1}=\frac{-18}{2}
=-9
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+25}{2*1}=\frac{32}{2}
=16
$