9/4x-5/6=13/2x

Solution for 9/4x-5/6=13/2x equation:

9/4x-5/6=13/2x

We move all terms to the left:

9/4x-5/6-(13/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9/4x-(+13/2x)-5/6=0

We get rid of parentheses

9/4x-13/2x-5/6=0

We calculate fractions


(-80x^2)/288x^2+648x/288x^2+(-1872x)/288x^2=0

We multiply all the terms by the denominator


(-80x^2)+648x+(-1872x)=0

We get rid of parentheses

-80x^2+648x-1872x=0

We add all the numbers together, and all the variables

-80x^2-1224x=0

a = -80; b = -1224; c = 0;
Δ = b2-4ac
Δ = -12242-4·(-80)·0
Δ = 1498176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1498176}=1224$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1224)-1224}{2*-80}=\frac{0}{-160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1224)+1224}{2*-80}=\frac{2448}{-160}
=-15+3/10
$