1/4k=-1k+9

Solution for 1/4k=-1k+9 equation:

1/4k=-1k+9

We move all terms to the left:

1/4k-(-1k+9)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R


We get rid of parentheses

1/4k+1k-9=0

We multiply all the terms by the denominator


1k*4k-9*4k+1=0

Wy multiply elements

4k^2-36k+1=0

a = 4; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·4·1
Δ = 1280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-16\sqrt{5}}{2*4}=\frac{36-16\sqrt{5}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+16\sqrt{5}}{2*4}=\frac{36+16\sqrt{5}}{8}
$