2k-3/k=9=3/5

Solution for 2k-3/k=9=3/5 equation:

2k-3/k=9=3/5

We move all terms to the left:

2k-3/k-(9)=0


Domain of the equation: k!=0

k∈R


We multiply all the terms by the denominator


2k*k-9*k-3=0

We add all the numbers together, and all the variables

-9k+2k*k-3=0

Wy multiply elements

2k^2-9k-3=0

a = 2; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·2·(-3)
Δ = 105
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{-(-9)-\sqrt{105}}{2*2}=\frac{9-\sqrt{105}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*2}=\frac{9+\sqrt{105}}{4}
$