7/10k=21k=

Solution for 7/10k=21k= equation:

7/10k=21k=

We move all terms to the left:

7/10k-(21k)=0


Domain of the equation: 10k!=0

k!=0/10

k!=0

k∈R


We add all the numbers together, and all the variables

-21k+7/10k=0

We multiply all the terms by the denominator


-21k*10k+7=0

Wy multiply elements

-210k^2+7=0

a = -210; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-210)·7
Δ = 5880
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:

$\sqrt{\Delta}=\sqrt{5880}=\sqrt{196*30}=\sqrt{196}*\sqrt{30}=14\sqrt{30}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{30}}{2*-210}=\frac{0-14\sqrt{30}}{-420}
=-\frac{14\sqrt{30}}{-420}
=-\frac{\sqrt{30}}{-30}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{30}}{2*-210}=\frac{0+14\sqrt{30}}{-420}
=\frac{14\sqrt{30}}{-420}
=\frac{\sqrt{30}}{-30}
$