8/3k+5=2k

Solution for 8/3k+5=2k equation:

8/3k+5=2k

We move all terms to the left:

8/3k+5-(2k)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We add all the numbers together, and all the variables

-2k+8/3k+5=0

We multiply all the terms by the denominator


-2k*3k+5*3k+8=0

Wy multiply elements

-6k^2+15k+8=0

a = -6; b = 15; c = +8;
Δ = b2-4ac
Δ = 152-4·(-6)·8
Δ = 417
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{-(15)-\sqrt{417}}{2*-6}=\frac{-15-\sqrt{417}}{-12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{417}}{2*-6}=\frac{-15+\sqrt{417}}{-12}
$