1/3*z=12

Solution for 1/3*z=12 equation:

1/3*z=12

We move all terms to the left:

1/3*z-(12)=0


Domain of the equation: 3*z!=0

z!=0/1

z!=0

z∈R


We multiply all the terms by the denominator


-12*3*z+1=0

Wy multiply elements

-36z*z+1=0

Wy multiply elements

-36z^2+1=0

a = -36; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-36)·1
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*-36}=\frac{-12}{-72}
=1/6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*-36}=\frac{12}{-72}
=-1/6
$