F/x=12-5x

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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 $

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