z/2z+6=3z+1

Solution for z/2z+6=3z+1 equation:

z/2z+6=3z+1

We move all terms to the left:

z/2z+6-(3z+1)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We get rid of parentheses

z/2z-3z-1+6=0

We multiply all the terms by the denominator


z-3z*2z-1*2z+6*2z=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-6z^2+11z=0

a = -6; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-6)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-6}=\frac{-22}{-12}
=1+5/6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-6}=\frac{0}{-12}
=0
$