8/3z+2z-6=3z+11

Solution for 8/3z+2z-6=3z+11 equation:

8/3z+2z-6=3z+11

We move all terms to the left:

8/3z+2z-6-(3z+11)=0


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R


We add all the numbers together, and all the variables

2z+8/3z-(3z+11)-6=0

We get rid of parentheses

2z+8/3z-3z-11-6=0

We multiply all the terms by the denominator


2z*3z-3z*3z-11*3z-6*3z+8=0

Wy multiply elements

6z^2-9z^2-33z-18z+8=0

We add all the numbers together, and all the variables

-3z^2-51z+8=0

a = -3; b = -51; c = +8;
Δ = b2-4ac
Δ = -512-4·(-3)·8
Δ = 2697
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{2697}}{2*-3}=\frac{51-\sqrt{2697}}{-6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2697}}{2*-3}=\frac{51+\sqrt{2697}}{-6}
$