2x-3/x+2=0.333

Solution for 2x-3/x+2=0.333 equation:

2x-3/x+2=0.333

We move all terms to the left:

2x-3/x+2-(0.333)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x-3/x+1.667=0

We multiply all the terms by the denominator


2x*x+(1.667)*x-3=0

We multiply parentheses

2x*x+1.667x-3=0

Wy multiply elements

2x^2+1.667x-3=0

a = 2; b = 1.667; c = -3;
Δ = b2-4ac
Δ = 1.6672-4·2·(-3)
Δ = 26.778889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.667)-\sqrt{26.778889}}{2*2}=\frac{-1.667-\sqrt{26.778889}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.667)+\sqrt{26.778889}}{2*2}=\frac{-1.667+\sqrt{26.778889}}{4}
$