9/2x-5/4=19/18x

Solution for 9/2x-5/4=19/18x equation:

9/2x-5/4=19/18x

We move all terms to the left:

9/2x-5/4-(19/18x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 18x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/2x-(+19/18x)-5/4=0

We get rid of parentheses

9/2x-19/18x-5/4=0

We calculate fractions


(-180x^2)/576x^2+2592x/576x^2+(-608x)/576x^2=0

We multiply all the terms by the denominator


(-180x^2)+2592x+(-608x)=0

We get rid of parentheses

-180x^2+2592x-608x=0

We add all the numbers together, and all the variables

-180x^2+1984x=0

a = -180; b = 1984; c = 0;
Δ = b2-4ac
Δ = 19842-4·(-180)·0
Δ = 3936256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3936256}=1984$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1984)-1984}{2*-180}=\frac{-3968}{-360}
=11+1/45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1984)+1984}{2*-180}=\frac{0}{-360}
=0
$