X-2=4x-9/x

Solution for X-2=4x-9/x equation:

X-2=4X-9/X

We move all terms to the left:

X-2-(4X-9/X)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+4X-9/X)-2=0

We get rid of parentheses

X-4X+9/X-2=0

We multiply all the terms by the denominator


X*X-4X*X-2*X+9=0

We add all the numbers together, and all the variables

-2X+X*X-4X*X+9=0

Wy multiply elements

X^2-4X^2-2X+9=0

We add all the numbers together, and all the variables

-3X^2-2X+9=0

a = -3; b = -2; c = +9;
Δ = b2-4ac
Δ = -22-4·(-3)·9
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{7}}{2*-3}=\frac{2-4\sqrt{7}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{7}}{2*-3}=\frac{2+4\sqrt{7}}{-6}
$