1/3z-2=6-3/4z

Solution for 1/3z-2=6-3/4z equation:

1/3z-2=6-3/4z

We move all terms to the left:

1/3z-2-(6-3/4z)=0


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R



Domain of the equation: 4z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

1/3z-(-3/4z+6)-2=0

We get rid of parentheses

1/3z+3/4z-6-2=0

We calculate fractions


4z/12z^2+9z/12z^2-6-2=0

We add all the numbers together, and all the variables

4z/12z^2+9z/12z^2-8=0

We multiply all the terms by the denominator


4z+9z-8*12z^2=0

We add all the numbers together, and all the variables

13z-8*12z^2=0

Wy multiply elements

-96z^2+13z=0

a = -96; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-96)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-96}=\frac{-26}{-192}
=13/96
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-96}=\frac{0}{-192}
=0
$