-3/8k-5-4=-5-6/7k

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Solution for -3/8k-5-4=-5-6/7k equation:



-3/8k-5-4=-5-6/7k
We move all terms to the left:
-3/8k-5-4-(-5-6/7k)=0
Domain of the equation: 8k!=0
k!=0/8
k!=0
k∈R
Domain of the equation: 7k)!=0
k!=0/1
k!=0
k∈R
We add all the numbers together, and all the variables
-3/8k-(-6/7k-5)-5-4=0
We add all the numbers together, and all the variables
-3/8k-(-6/7k-5)-9=0
We get rid of parentheses
-3/8k+6/7k+5-9=0
We calculate fractions
(-21k)/56k^2+48k/56k^2+5-9=0
We add all the numbers together, and all the variables
(-21k)/56k^2+48k/56k^2-4=0
We multiply all the terms by the denominator
(-21k)+48k-4*56k^2=0
We add all the numbers together, and all the variables
48k+(-21k)-4*56k^2=0
Wy multiply elements
-224k^2+48k+(-21k)=0
We get rid of parentheses
-224k^2+48k-21k=0
We add all the numbers together, and all the variables
-224k^2+27k=0
a = -224; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-224)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-224}=\frac{-54}{-448} =27/224 $
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-224}=\frac{0}{-448} =0 $

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