15(1/3)z=5

Solution for 15(1/3)z=5 equation:

15(1/3)z=5

We move all terms to the left:

15(1/3)z-(5)=0


Domain of the equation: 3)z!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

15(+1/3)z-5=0

We multiply parentheses

15z^2-5=0

a = 15; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·15·(-5)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*15}=\frac{0-10\sqrt{3}}{30}
=-\frac{10\sqrt{3}}{30}
=-\frac{\sqrt{3}}{3}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*15}=\frac{0+10\sqrt{3}}{30}
=\frac{10\sqrt{3}}{30}
=\frac{\sqrt{3}}{3}
$