3/2z-2=13/4z-9

Solution for 3/2z-2=13/4z-9 equation:

3/2z-2=13/4z-9

We move all terms to the left:

3/2z-2-(13/4z-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

3/2z-13/4z+9-2=0

We calculate fractions


12z/8z^2+(-26z)/8z^2+9-2=0

We add all the numbers together, and all the variables

12z/8z^2+(-26z)/8z^2+7=0

We multiply all the terms by the denominator


12z+(-26z)+7*8z^2=0

Wy multiply elements

56z^2+12z+(-26z)=0

We get rid of parentheses

56z^2+12z-26z=0

We add all the numbers together, and all the variables

56z^2-14z=0

a = 56; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·56·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*56}=\frac{0}{112}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*56}=\frac{28}{112}
=1/4
$