7/3z-2=3z-9

Solution for 7/3z-2=3z-9 equation:

7/3z-2=3z-9

We move all terms to the left:

7/3z-2-(3z-9)=0


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R


We get rid of parentheses

7/3z-3z+9-2=0

We multiply all the terms by the denominator


-3z*3z+9*3z-2*3z+7=0

Wy multiply elements

-9z^2+27z-6z+7=0

We add all the numbers together, and all the variables

-9z^2+21z+7=0

a = -9; b = 21; c = +7;
Δ = b2-4ac
Δ = 212-4·(-9)·7
Δ = 693
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{693}=\sqrt{9*77}=\sqrt{9}*\sqrt{77}=3\sqrt{77}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{77}}{2*-9}=\frac{-21-3\sqrt{77}}{-18}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{77}}{2*-9}=\frac{-21+3\sqrt{77}}{-18}
$