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(F)=5/11F+10
We move all terms to the left:
(F)-(5/11F+10)=0
Domain of the equation: 11F+10)!=0We get rid of parentheses
F∈R
F-5/11F-10=0
We multiply all the terms by the denominator
F*11F-10*11F-5=0
Wy multiply elements
11F^2-110F-5=0
a = 11; b = -110; c = -5;
Δ = b2-4ac
Δ = -1102-4·11·(-5)
Δ = 12320
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}$$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12320}=\sqrt{16*770}=\sqrt{16}*\sqrt{770}=4\sqrt{770}$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-4\sqrt{770}}{2*11}=\frac{110-4\sqrt{770}}{22} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+4\sqrt{770}}{2*11}=\frac{110+4\sqrt{770}}{22} $
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