4/2k+5=2-3/k+2

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Solution for 4/2k+5=2-3/k+2 equation:



4/2k+5=2-3/k+2
We move all terms to the left:
4/2k+5-(2-3/k+2)=0
Domain of the equation: 2k!=0
k!=0/2
k!=0
k∈R
Domain of the equation: k+2)!=0
k∈R
We add all the numbers together, and all the variables
4/2k-(-3/k+4)+5=0
We get rid of parentheses
4/2k+3/k-4+5=0
We calculate fractions
4k/2k^2+6k/2k^2-4+5=0
We add all the numbers together, and all the variables
4k/2k^2+6k/2k^2+1=0
We multiply all the terms by the denominator
4k+6k+1*2k^2=0
We add all the numbers together, and all the variables
10k+1*2k^2=0
Wy multiply elements
2k^2+10k=0
a = 2; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·2·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*2}=\frac{-20}{4} =-5 $
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*2}=\frac{0}{4} =0 $

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