5k-2/k=18

Solution for 5k-2/k=18 equation:

5k-2/k=18

We move all terms to the left:

5k-2/k-(18)=0


Domain of the equation: k!=0

k∈R


We multiply all the terms by the denominator


5k*k-18*k-2=0

We add all the numbers together, and all the variables

-18k+5k*k-2=0

Wy multiply elements

5k^2-18k-2=0

a = 5; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·5·(-2)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{91}}{2*5}=\frac{18-2\sqrt{91}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{91}}{2*5}=\frac{18+2\sqrt{91}}{10}
$