-5/8k+1/2=-1+6/7k

Solution for -5/8k+1/2=-1+6/7k equation:

-5/8k+1/2=-1+6/7k

We move all terms to the left:

-5/8k+1/2-(-1+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

-5/8k-(6/7k-1)+1/2=0

We get rid of parentheses

-5/8k-6/7k+1+1/2=0

We calculate fractions


392k^2/224k^2+(-140k)/224k^2+(-192k)/224k^2+1=0

We multiply all the terms by the denominator


392k^2+(-140k)+(-192k)+1*224k^2=0

Wy multiply elements

392k^2+224k^2+(-140k)+(-192k)=0

We get rid of parentheses

392k^2+224k^2-140k-192k=0

We add all the numbers together, and all the variables

616k^2-332k=0

a = 616; b = -332; c = 0;
Δ = b2-4ac
Δ = -3322-4·616·0
Δ = 110224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{110224}=332$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-332)-332}{2*616}=\frac{0}{1232}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-332)+332}{2*616}=\frac{664}{1232}
=83/154
$