3x-5/x-0.5=-2

Solution for 3x-5/x-0.5=-2 equation:

3x-5/x-0.5=-2

We move all terms to the left:

3x-5/x-0.5-(-2)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-5/x+1.5=0

We multiply all the terms by the denominator


3x*x+(1.5)*x-5=0

We multiply parentheses

3x*x+1.5x-5=0

Wy multiply elements

3x^2+1.5x-5=0

a = 3; b = 1.5; c = -5;
Δ = b2-4ac
Δ = 1.52-4·3·(-5)
Δ = 62.25
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{-(1.5)-\sqrt{62.25}}{2*3}=\frac{-1.5-\sqrt{62.25}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{62.25}}{2*3}=\frac{-1.5+\sqrt{62.25}}{6}
$