1/2z+3=1/33z-5

Solution for 1/2z+3=1/33z-5 equation:

1/2z+3=1/33z-5

We move all terms to the left:

1/2z+3-(1/33z-5)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 33z-5)!=0

z∈R


We get rid of parentheses

1/2z-1/33z+5+3=0

We calculate fractions


33z/66z^2+(-2z)/66z^2+5+3=0

We add all the numbers together, and all the variables

33z/66z^2+(-2z)/66z^2+8=0

We multiply all the terms by the denominator


33z+(-2z)+8*66z^2=0

Wy multiply elements

528z^2+33z+(-2z)=0

We get rid of parentheses

528z^2+33z-2z=0

We add all the numbers together, and all the variables

528z^2+31z=0

a = 528; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·528·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*528}=\frac{-62}{1056}
=-31/528
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*528}=\frac{0}{1056}
=0
$