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(F)=2/3F+7
We move all terms to the left:
(F)-(2/3F+7)=0
Domain of the equation: 3F+7)!=0We get rid of parentheses
F∈R
F-2/3F-7=0
We multiply all the terms by the denominator
F*3F-7*3F-2=0
Wy multiply elements
3F^2-21F-2=0
a = 3; b = -21; c = -2;
Δ = b2-4ac
Δ = -212-4·3·(-2)
Δ = 465
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{-(-21)-\sqrt{465}}{2*3}=\frac{21-\sqrt{465}}{6} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{465}}{2*3}=\frac{21+\sqrt{465}}{6} $
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