1/2z+5=1/6z+6

Solution for 1/2z+5=1/6z+6 equation:

1/2z+5=1/6z+6

We move all terms to the left:

1/2z+5-(1/6z+6)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 6z+6)!=0

z∈R


We get rid of parentheses

1/2z-1/6z-6+5=0

We calculate fractions


6z/12z^2+(-2z)/12z^2-6+5=0

We add all the numbers together, and all the variables

6z/12z^2+(-2z)/12z^2-1=0

We multiply all the terms by the denominator


6z+(-2z)-1*12z^2=0

Wy multiply elements

-12z^2+6z+(-2z)=0

We get rid of parentheses

-12z^2+6z-2z=0

We add all the numbers together, and all the variables

-12z^2+4z=0

a = -12; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-12}=\frac{-8}{-24}
=1/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-12}=\frac{0}{-24}
=0
$