6/k-4=8/7k+9

Solution for 6/k-4=8/7k+9 equation:

6/k-4=8/7k+9

We move all terms to the left:

6/k-4-(8/7k+9)=0


Domain of the equation: k!=0

k∈R



Domain of the equation: 7k+9)!=0

k∈R


We get rid of parentheses

6/k-8/7k-9-4=0

We calculate fractions


42k/7k^2+(-8k)/7k^2-9-4=0

We add all the numbers together, and all the variables

42k/7k^2+(-8k)/7k^2-13=0

We multiply all the terms by the denominator


42k+(-8k)-13*7k^2=0

Wy multiply elements

-91k^2+42k+(-8k)=0

We get rid of parentheses

-91k^2+42k-8k=0

We add all the numbers together, and all the variables

-91k^2+34k=0

a = -91; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-91)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-91}=\frac{-68}{-182}
=34/91
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-91}=\frac{0}{-182}
=0
$