2/9k+4/3=8+9/8k

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Solution for 2/9k+4/3=8+9/8k equation:



2/9k+4/3=8+9/8k
We move all terms to the left:
2/9k+4/3-(8+9/8k)=0
Domain of the equation: 9k!=0
k!=0/9
k!=0
k∈R
Domain of the equation: 8k)!=0
k!=0/1
k!=0
k∈R
We add all the numbers together, and all the variables
2/9k-(9/8k+8)+4/3=0
We get rid of parentheses
2/9k-9/8k-8+4/3=0
We calculate fractions
2304k^2/648k^2+144k/648k^2+(-729k)/648k^2-8=0
We multiply all the terms by the denominator
2304k^2+144k+(-729k)-8*648k^2=0
Wy multiply elements
2304k^2-5184k^2+144k+(-729k)=0
We get rid of parentheses
2304k^2-5184k^2+144k-729k=0
We add all the numbers together, and all the variables
-2880k^2-585k=0
a = -2880; b = -585; c = 0;
Δ = b2-4ac
Δ = -5852-4·(-2880)·0
Δ = 342225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{342225}=585$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-585)-585}{2*-2880}=\frac{0}{-5760} =0 $
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-585)+585}{2*-2880}=\frac{1170}{-5760} =-13/64 $

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