F(x)=6x+5/2x-20

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Solution for F(x)=6x+5/2x-20 equation:



(F)=6F+5/2F-20
We move all terms to the left:
(F)-(6F+5/2F-20)=0
Domain of the equation: 2F-20)!=0
F∈R
We get rid of parentheses
F-6F-5/2F+20=0
We multiply all the terms by the denominator
F*2F-6F*2F+20*2F-5=0
Wy multiply elements
2F^2-12F^2+40F-5=0
We add all the numbers together, and all the variables
-10F^2+40F-5=0
a = -10; b = 40; c = -5;
Δ = b2-4ac
Δ = 402-4·(-10)·(-5)
Δ = 1400
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:
$\sqrt{\Delta}=\sqrt{1400}=\sqrt{100*14}=\sqrt{100}*\sqrt{14}=10\sqrt{14}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{14}}{2*-10}=\frac{-40-10\sqrt{14}}{-20} $
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{14}}{2*-10}=\frac{-40+10\sqrt{14}}{-20} $

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