2x-9/x=8-3x

Solution for 2x-9/x=8-3x equation:

2x-9/x=8-3x

We move all terms to the left:

2x-9/x-(8-3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-9/x-(-3x+8)=0

We get rid of parentheses

2x-9/x+3x-8=0

We multiply all the terms by the denominator


2x*x+3x*x-8*x-9=0

We add all the numbers together, and all the variables

-8x+2x*x+3x*x-9=0

Wy multiply elements

2x^2+3x^2-8x-9=0

We add all the numbers together, and all the variables

5x^2-8x-9=0

a = 5; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·5·(-9)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{61}}{2*5}=\frac{8-2\sqrt{61}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{61}}{2*5}=\frac{8+2\sqrt{61}}{10}
$