F(7)=14/x2

Solution for F(7)=14/x2 equation:

(7)=14/F2

We move all terms to the left:

(7)-(14/F2)=0


Domain of the equation: F2)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

-(+14/F2)+7=0

We get rid of parentheses

-14/F2+7=0

We multiply all the terms by the denominator


7*F2-14=0

We add all the numbers together, and all the variables

7F^2-14=0

a = 7; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·7·(-14)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{2}}{2*7}=\frac{0-14\sqrt{2}}{14}
=-\frac{14\sqrt{2}}{14}
=-\sqrt{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{2}}{2*7}=\frac{0+14\sqrt{2}}{14}
=\frac{14\sqrt{2}}{14}
=\sqrt{2}
$