2.6(2x+3)=5/2x

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Solution for 2.6(2x+3)=5/2x equation:



2.6(2x+3)=5/2x
We move all terms to the left:
2.6(2x+3)-(5/2x)=0
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2.6(2x+3)-(+5/2x)=0
We multiply parentheses
5.2x-(+5/2x)+7.8=0
We get rid of parentheses
5.2x-5/2x+7.8=0
We multiply all the terms by the denominator
(5.2x)*2x+(7.8)*2x-5=0
We add all the numbers together, and all the variables
(+5.2x)*2x+(7.8)*2x-5=0
We multiply parentheses
10x^2+15.6x-5=0
a = 10; b = 15.6; c = -5;
Δ = b2-4ac
Δ = 15.62-4·10·(-5)
Δ = 443.36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15.6)-\sqrt{443.36}}{2*10}=\frac{-15.6-\sqrt{443.36}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15.6)+\sqrt{443.36}}{2*10}=\frac{-15.6+\sqrt{443.36}}{20} $

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