9/k-7=k

Solution for 9/k-7=k equation:

9/k-7=k

We move all terms to the left:

9/k-7-(k)=0


Domain of the equation: k!=0

k∈R


We add all the numbers together, and all the variables

-1k+9/k-7=0

We multiply all the terms by the denominator


-1k*k-7*k+9=0

We add all the numbers together, and all the variables

-7k-1k*k+9=0

Wy multiply elements

-1k^2-7k+9=0

a = -1; b = -7; c = +9;
Δ = b2-4ac
Δ = -72-4·(-1)·9
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{85}}{2*-1}=\frac{7-\sqrt{85}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{85}}{2*-1}=\frac{7+\sqrt{85}}{-2}
$