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(F)=2F+7/3F-13
We move all terms to the left:
(F)-(2F+7/3F-13)=0
Domain of the equation: 3F-13)!=0We get rid of parentheses
F∈R
F-2F-7/3F+13=0
We multiply all the terms by the denominator
F*3F-2F*3F+13*3F-7=0
Wy multiply elements
3F^2-6F^2+39F-7=0
We add all the numbers together, and all the variables
-3F^2+39F-7=0
a = -3; b = 39; c = -7;
Δ = b2-4ac
Δ = 392-4·(-3)·(-7)
Δ = 1437
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}$$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-\sqrt{1437}}{2*-3}=\frac{-39-\sqrt{1437}}{-6} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{1437}}{2*-3}=\frac{-39+\sqrt{1437}}{-6} $
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