-9/8k+6/7=-2-7/3k

Solution for -9/8k+6/7=-2-7/3k equation:

-9/8k+6/7=-2-7/3k

We move all terms to the left:

-9/8k+6/7-(-2-7/3k)=0


Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R



Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-9/8k-(-7/3k-2)+6/7=0

We get rid of parentheses

-9/8k+7/3k+2+6/7=0

We calculate fractions


432k^2/1176k^2+(-1323k)/1176k^2+2744k/1176k^2+2=0

We multiply all the terms by the denominator


432k^2+(-1323k)+2744k+2*1176k^2=0

We add all the numbers together, and all the variables

432k^2+2744k+(-1323k)+2*1176k^2=0

Wy multiply elements

432k^2+2352k^2+2744k+(-1323k)=0

We get rid of parentheses

432k^2+2352k^2+2744k-1323k=0

We add all the numbers together, and all the variables

2784k^2+1421k=0

a = 2784; b = 1421; c = 0;
Δ = b2-4ac
Δ = 14212-4·2784·0
Δ = 2019241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2019241}=1421$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1421)-1421}{2*2784}=\frac{-2842}{5568}
=-49/96
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1421)+1421}{2*2784}=\frac{0}{5568}
=0
$