10/15k-k-3/15k=1/15k+3

Solution for 10/15k-k-3/15k=1/15k+3 equation:

10/15k-k-3/15k=1/15k+3

We move all terms to the left:

10/15k-k-3/15k-(1/15k+3)=0


Domain of the equation: 15k!=0

k!=0/15

k!=0

k∈R



Domain of the equation: 15k+3)!=0

k∈R


We add all the numbers together, and all the variables

-1k+10/15k-3/15k-(1/15k+3)=0

We get rid of parentheses

-1k+10/15k-3/15k-1/15k-3=0

We multiply all the terms by the denominator


-1k*15k-3*15k+10-3-1=0

We add all the numbers together, and all the variables

-1k*15k-3*15k+6=0

Wy multiply elements

-15k^2-45k+6=0

a = -15; b = -45; c = +6;
Δ = b2-4ac
Δ = -452-4·(-15)·6
Δ = 2385
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:

$\sqrt{\Delta}=\sqrt{2385}=\sqrt{9*265}=\sqrt{9}*\sqrt{265}=3\sqrt{265}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{265}}{2*-15}=\frac{45-3\sqrt{265}}{-30}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{265}}{2*-15}=\frac{45+3\sqrt{265}}{-30}
$