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(F)=2F-8/7F+2
We move all terms to the left:
(F)-(2F-8/7F+2)=0
Domain of the equation: 7F+2)!=0We get rid of parentheses
F∈R
F-2F+8/7F-2=0
We multiply all the terms by the denominator
F*7F-2F*7F-2*7F+8=0
Wy multiply elements
7F^2-14F^2-14F+8=0
We add all the numbers together, and all the variables
-7F^2-14F+8=0
a = -7; b = -14; c = +8;
Δ = b2-4ac
Δ = -142-4·(-7)·8
Δ = 420
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}$$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{105}}{2*-7}=\frac{14-2\sqrt{105}}{-14} $$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{105}}{2*-7}=\frac{14+2\sqrt{105}}{-14} $
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