1/3+(8/45)z=15

Solution for 1/3+(8/45)z=15 equation:

1/3+(8/45)z=15

We move all terms to the left:

1/3+(8/45)z-(15)=0


Domain of the equation: 45)z!=0

z!=0/1

z!=0

z∈R


determiningTheFunctionDomain
(8/45)z-15+1/3=0

We add all the numbers together, and all the variables

(+8/45)z-15+1/3=0

We multiply parentheses

8z^2-15+1/3=0

We multiply all the terms by the denominator


8z^2*3+1-15*3=0

We add all the numbers together, and all the variables

8z^2*3-44=0

Wy multiply elements

24z^2-44=0

a = 24; b = 0; c = -44;
Δ = b2-4ac
Δ = 02-4·24·(-44)
Δ = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{66}}{2*24}=\frac{0-8\sqrt{66}}{48}
=-\frac{8\sqrt{66}}{48}
=-\frac{\sqrt{66}}{6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{66}}{2*24}=\frac{0+8\sqrt{66}}{48}
=\frac{8\sqrt{66}}{48}
=\frac{\sqrt{66}}{6}
$