-2/x+3=5/2x+2

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

-2/x+3=5/2x+2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+2)!=0

x∈R


We get rid of parentheses

-2/x-5/2x-2+3=0

We calculate fractions


(-4x)/2x^2+(-5x)/2x^2-2+3=0

We add all the numbers together, and all the variables

(-4x)/2x^2+(-5x)/2x^2+1=0

We multiply all the terms by the denominator


(-4x)+(-5x)+1*2x^2=0

Wy multiply elements

2x^2+(-4x)+(-5x)=0

We get rid of parentheses

2x^2-4x-5x=0

We add all the numbers together, and all the variables

2x^2-9x=0

a = 2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·2·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*2}=\frac{18}{4}
=4+1/2
$