6/z-2=-5/3z+4

Solution for 6/z-2=-5/3z+4 equation:

6/z-2=-5/3z+4

We move all terms to the left:

6/z-2-(-5/3z+4)=0


Domain of the equation: z!=0

z∈R



Domain of the equation: 3z+4)!=0

z∈R


We get rid of parentheses

6/z+5/3z-4-2=0

We calculate fractions


18z/3z^2+5z/3z^2-4-2=0

We add all the numbers together, and all the variables

18z/3z^2+5z/3z^2-6=0

We multiply all the terms by the denominator


18z+5z-6*3z^2=0

We add all the numbers together, and all the variables

23z-6*3z^2=0

Wy multiply elements

-18z^2+23z=0

a = -18; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-18)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-18}=\frac{-46}{-36}
=1+5/18
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-18}=\frac{0}{-36}
=0
$