30/k-32k=3

Solution for 30/k-32k=3 equation:

30/k-32k=3

We move all terms to the left:

30/k-32k-(3)=0


Domain of the equation: k!=0

k∈R


We add all the numbers together, and all the variables

-32k+30/k-3=0

We multiply all the terms by the denominator


-32k*k-3*k+30=0

We add all the numbers together, and all the variables

-3k-32k*k+30=0

Wy multiply elements

-32k^2-3k+30=0

a = -32; b = -3; c = +30;
Δ = b2-4ac
Δ = -32-4·(-32)·30
Δ = 3849
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{-(-3)-\sqrt{3849}}{2*-32}=\frac{3-\sqrt{3849}}{-64}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{3849}}{2*-32}=\frac{3+\sqrt{3849}}{-64}
$