4/X-2-7/2x-4=5/2

Solution for 4/X-2-7/2x-4=5/2 equation:

4/X-2-7/2X-4=5/2

We move all terms to the left:

4/X-2-7/2X-4-(5/2)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

4/X-7/2X-2-4-(+5/2)=0

We add all the numbers together, and all the variables

4/X-7/2X-6-(+5/2)=0

We get rid of parentheses

4/X-7/2X-6-5/2=0

We calculate fractions


32X/8X^2+(-7X)/8X^2+(-5X)/8X^2-6=0

We multiply all the terms by the denominator


32X+(-7X)+(-5X)-6*8X^2=0

Wy multiply elements

-48X^2+32X+(-7X)+(-5X)=0

We get rid of parentheses

-48X^2+32X-7X-5X=0

We add all the numbers together, and all the variables

-48X^2+20X=0

a = -48; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-48)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-48}=\frac{-40}{-96}
=5/12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-48}=\frac{0}{-96}
=0
$