1/15z=6z=

Solution for 1/15z=6z= equation:

1/15z=6z=

We move all terms to the left:

1/15z-(6z)=0


Domain of the equation: 15z!=0

z!=0/15

z!=0

z∈R


We add all the numbers together, and all the variables

-6z+1/15z=0

We multiply all the terms by the denominator


-6z*15z+1=0

Wy multiply elements

-90z^2+1=0

a = -90; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-90)·1
Δ = 360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*-90}=\frac{0-6\sqrt{10}}{-180}
=-\frac{6\sqrt{10}}{-180}
=-\frac{\sqrt{10}}{-30}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*-90}=\frac{0+6\sqrt{10}}{-180}
=\frac{6\sqrt{10}}{-180}
=\frac{\sqrt{10}}{-30}
$