5/12z-7/18z=2

Solution for 5/12z-7/18z=2 equation:

5/12z-7/18z=2

We move all terms to the left:

5/12z-7/18z-(2)=0


Domain of the equation: 12z!=0

z!=0/12

z!=0

z∈R



Domain of the equation: 18z!=0

z!=0/18

z!=0

z∈R


We calculate fractions


90z/216z^2+(-84z)/216z^2-2=0

We multiply all the terms by the denominator


90z+(-84z)-2*216z^2=0

Wy multiply elements

-432z^2+90z+(-84z)=0

We get rid of parentheses

-432z^2+90z-84z=0

We add all the numbers together, and all the variables

-432z^2+6z=0

a = -432; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-432)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-432}=\frac{-12}{-864}
=1/72
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-432}=\frac{0}{-864}
=0
$