5/6z=10z=10

Solution for 5/6z=10z=10 equation:

5/6z=10z=10

We move all terms to the left:

5/6z-(10z)=0


Domain of the equation: 6z!=0

z!=0/6

z!=0

z∈R


We add all the numbers together, and all the variables

-10z+5/6z=0

We multiply all the terms by the denominator


-10z*6z+5=0

Wy multiply elements

-60z^2+5=0

a = -60; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-60)·5
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*-60}=\frac{0-20\sqrt{3}}{-120}
=-\frac{20\sqrt{3}}{-120}
=-\frac{\sqrt{3}}{-6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*-60}=\frac{0+20\sqrt{3}}{-120}
=\frac{20\sqrt{3}}{-120}
=\frac{\sqrt{3}}{-6}
$