5/6z=6-11/12z

Solution for 5/6z=6-11/12z equation:

5/6z=6-11/12z

We move all terms to the left:

5/6z-(6-11/12z)=0


Domain of the equation: 6z!=0

z!=0/6

z!=0

z∈R



Domain of the equation: 12z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

5/6z-(-11/12z+6)=0

We get rid of parentheses

5/6z+11/12z-6=0

We calculate fractions


60z/72z^2+66z/72z^2-6=0

We multiply all the terms by the denominator


60z+66z-6*72z^2=0

We add all the numbers together, and all the variables

126z-6*72z^2=0

Wy multiply elements

-432z^2+126z=0

a = -432; b = 126; c = 0;
Δ = b2-4ac
Δ = 1262-4·(-432)·0
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-126}{2*-432}=\frac{-252}{-864}
=7/24
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+126}{2*-432}=\frac{0}{-864}
=0
$