13/4-2/x=3-5/2x

Solution for 13/4-2/x=3-5/2x equation:

13/4-2/x=3-5/2x

We move all terms to the left:

13/4-2/x-(3-5/2x)=0


Domain of the equation: 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

-2/x-(-5/2x+3)+13/4=0

We get rid of parentheses

-2/x+5/2x-3+13/4=0

We calculate fractions


52x^2/32x^2+(-64x)/32x^2+80x/32x^2-3=0

We multiply all the terms by the denominator


52x^2+(-64x)+80x-3*32x^2=0

We add all the numbers together, and all the variables

52x^2+80x+(-64x)-3*32x^2=0

Wy multiply elements

52x^2-96x^2+80x+(-64x)=0

We get rid of parentheses

52x^2-96x^2+80x-64x=0

We add all the numbers together, and all the variables

-44x^2+16x=0

a = -44; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-44)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-44}=\frac{-32}{-88}
=4/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-44}=\frac{0}{-88}
=0
$