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(F)=8F-2/7F-8
We move all terms to the left:
(F)-(8F-2/7F-8)=0
Domain of the equation: 7F-8)!=0We get rid of parentheses
F∈R
F-8F+2/7F+8=0
We multiply all the terms by the denominator
F*7F-8F*7F+8*7F+2=0
Wy multiply elements
7F^2-56F^2+56F+2=0
We add all the numbers together, and all the variables
-49F^2+56F+2=0
a = -49; b = 56; c = +2;
Δ = b2-4ac
Δ = 562-4·(-49)·2
Δ = 3528
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}$$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3528}=\sqrt{1764*2}=\sqrt{1764}*\sqrt{2}=42\sqrt{2}$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-42\sqrt{2}}{2*-49}=\frac{-56-42\sqrt{2}}{-98} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+42\sqrt{2}}{2*-49}=\frac{-56+42\sqrt{2}}{-98} $
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