X(2x+3)/x-4=44/x-4

Solution for X(2x+3)/x-4=44/x-4 equation:

X(2X+3)/X-4=44/X-4

We move all terms to the left:

X(2X+3)/X-4-(44/X-4)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X-4)!=0

X∈R


We get rid of parentheses

X(2X+3)/X-44/X+4-4=0

We multiply all the terms by the denominator


X(2X+3)+4*X-4*X-44=0

We add all the numbers together, and all the variables

X(2X+3)-44=0

We multiply parentheses

2X^2+3X-44=0

a = 2; b = 3; c = -44;
Δ = b2-4ac
Δ = 32-4·2·(-44)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-19}{2*2}=\frac{-22}{4}
=-5+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+19}{2*2}=\frac{16}{4}
=4
$