11/2z-2=31/4z-9

Solution for 11/2z-2=31/4z-9 equation:

11/2z-2=31/4z-9

We move all terms to the left:

11/2z-2-(31/4z-9)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 4z-9)!=0

z∈R


We get rid of parentheses

11/2z-31/4z+9-2=0

We calculate fractions


44z/8z^2+(-62z)/8z^2+9-2=0

We add all the numbers together, and all the variables

44z/8z^2+(-62z)/8z^2+7=0

We multiply all the terms by the denominator


44z+(-62z)+7*8z^2=0

Wy multiply elements

56z^2+44z+(-62z)=0

We get rid of parentheses

56z^2+44z-62z=0

We add all the numbers together, and all the variables

56z^2-18z=0

a = 56; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·56·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*56}=\frac{0}{112}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*56}=\frac{36}{112}
=9/28
$