F/x=12-5x

Solution for F/x=12-5x equation:

/F=12-5F

We move all terms to the left:

/F-(12-5F)=0


Domain of the equation: F!=0

F∈R


We add all the numbers together, and all the variables

/F-(-5F+12)=0

We get rid of parentheses

/F+5F-12=0

We multiply all the terms by the denominator


5F*F-12*F+=0

We add all the numbers together, and all the variables

-12F+5F*F=0

Wy multiply elements

5F^2-12F=0

a = 5; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·5·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*5}=\frac{0}{10}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*5}=\frac{24}{10}
=2+2/5
$