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F=12-6F/7F+12
We move all terms to the left:
F-(12-6F/7F+12)=0
Domain of the equation: 7F+12)!=0We add all the numbers together, and all the variables
F∈R
F-(-6F/7F+24)=0
We get rid of parentheses
F+6F/7F-24=0
We multiply all the terms by the denominator
F*7F+6F-24*7F=0
We add all the numbers together, and all the variables
6F+F*7F-24*7F=0
Wy multiply elements
7F^2+6F-168F=0
We add all the numbers together, and all the variables
7F^2-162F=0
a = 7; b = -162; c = 0;
Δ = b2-4ac
Δ = -1622-4·7·0
Δ = 26244
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{26244}=162$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-162}{2*7}=\frac{0}{14} =0 $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+162}{2*7}=\frac{324}{14} =23+1/7 $
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