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

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
$