8/9z-1/2=-2/3z+6=

Solution for 8/9z-1/2=-2/3z+6= equation:

8/9z-1/2=-2/3z+6=

We move all terms to the left:

8/9z-1/2-(-2/3z+6)=0


Domain of the equation: 9z!=0

z!=0/9

z!=0

z∈R



Domain of the equation: 3z+6)!=0

z∈R


We get rid of parentheses

8/9z+2/3z-6-1/2=0

We calculate fractions


(-81z^2)/108z^2+96z/108z^2+72z/108z^2-6=0

We multiply all the terms by the denominator


(-81z^2)+96z+72z-6*108z^2=0

We add all the numbers together, and all the variables

(-81z^2)+168z-6*108z^2=0

Wy multiply elements

(-81z^2)-648z^2+168z=0

We get rid of parentheses

-81z^2-648z^2+168z=0

We add all the numbers together, and all the variables

-729z^2+168z=0

a = -729; b = 168; c = 0;
Δ = b2-4ac
Δ = 1682-4·(-729)·0
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-168}{2*-729}=\frac{-336}{-1458}
=56/243
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+168}{2*-729}=\frac{0}{-1458}
=0
$