11/2z-2=31/3z-9

Solution for 11/2z-2=31/3z-9 equation:

11/2z-2=31/3z-9

We move all terms to the left:

11/2z-2-(31/3z-9)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 3z-9)!=0

z∈R


We get rid of parentheses

11/2z-31/3z+9-2=0

We calculate fractions


33z/6z^2+(-62z)/6z^2+9-2=0

We add all the numbers together, and all the variables

33z/6z^2+(-62z)/6z^2+7=0

We multiply all the terms by the denominator


33z+(-62z)+7*6z^2=0

Wy multiply elements

42z^2+33z+(-62z)=0

We get rid of parentheses

42z^2+33z-62z=0

We add all the numbers together, and all the variables

42z^2-29z=0

a = 42; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·42·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*42}=\frac{0}{84}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*42}=\frac{58}{84}
=29/42
$