(134/21)k=40/3

Solution for (134/21)k=40/3 equation:

(134/21)k=40/3

We move all terms to the left:

(134/21)k-(40/3)=0


Domain of the equation: 21)k!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

(+134/21)k-(+40/3)=0

We multiply parentheses

134k^2-(+40/3)=0

We get rid of parentheses

134k^2-40/3=0

We multiply all the terms by the denominator


134k^2*3-40=0

Wy multiply elements

402k^2-40=0

a = 402; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·402·(-40)
Δ = 64320
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:

$\sqrt{\Delta}=\sqrt{64320}=\sqrt{64*1005}=\sqrt{64}*\sqrt{1005}=8\sqrt{1005}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{1005}}{2*402}=\frac{0-8\sqrt{1005}}{804}
=-\frac{8\sqrt{1005}}{804}
=-\frac{2\sqrt{1005}}{201}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{1005}}{2*402}=\frac{0+8\sqrt{1005}}{804}
=\frac{8\sqrt{1005}}{804}
=\frac{2\sqrt{1005}}{201}
$