F(x)=x2-3x-1

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Solution for F(x)=x2-3x-1 equation:



(F)=F2-3F-1
We move all terms to the left:
(F)-(F2-3F-1)=0
We add all the numbers together, and all the variables
-(+F^2-3F-1)+F=0
We get rid of parentheses
-F^2+3F+F+1=0
We add all the numbers together, and all the variables
-1F^2+4F+1=0
a = -1; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-1)·1
Δ = 20
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:
$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{5}}{2*-1}=\frac{-4-2\sqrt{5}}{-2} $
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{5}}{2*-1}=\frac{-4+2\sqrt{5}}{-2} $

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