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

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

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

We move all terms to the left:

4/7k-7/6-(-8-5/8k)=0


Domain of the equation: 7k!=0

k!=0/7

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

4/7k-(-5/8k-8)-7/6=0

We get rid of parentheses

4/7k+5/8k+8-7/6=0

We calculate fractions


(-3136k^2)/2016k^2+1152k/2016k^2+1260k/2016k^2+8=0

We multiply all the terms by the denominator


(-3136k^2)+1152k+1260k+8*2016k^2=0

We add all the numbers together, and all the variables

(-3136k^2)+2412k+8*2016k^2=0

Wy multiply elements

(-3136k^2)+16128k^2+2412k=0

We get rid of parentheses

-3136k^2+16128k^2+2412k=0

We add all the numbers together, and all the variables

12992k^2+2412k=0

a = 12992; b = 2412; c = 0;
Δ = b2-4ac
Δ = 24122-4·12992·0
Δ = 5817744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5817744}=2412$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2412)-2412}{2*12992}=\frac{-4824}{25984}
=-603/3248
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2412)+2412}{2*12992}=\frac{0}{25984}
=0
$