2/3k+5/7=-1+1/8k

Solution for 2/3k+5/7=-1+1/8k equation:

2/3k+5/7=-1+1/8k

We move all terms to the left:

2/3k+5/7-(-1+1/8k)=0


Domain of the equation: 3k!=0

k!=0/3

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

2/3k-(1/8k-1)+5/7=0

We get rid of parentheses

2/3k-1/8k+1+5/7=0

We calculate fractions


960k^2/1176k^2+784k/1176k^2+(-147k)/1176k^2+1=0

We multiply all the terms by the denominator


960k^2+784k+(-147k)+1*1176k^2=0

Wy multiply elements

960k^2+1176k^2+784k+(-147k)=0

We get rid of parentheses

960k^2+1176k^2+784k-147k=0

We add all the numbers together, and all the variables

2136k^2+637k=0

a = 2136; b = 637; c = 0;
Δ = b2-4ac
Δ = 6372-4·2136·0
Δ = 405769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{405769}=637$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(637)-637}{2*2136}=\frac{-1274}{4272}
=-637/2136
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(637)+637}{2*2136}=\frac{0}{4272}
=0
$