2x+1=3/2x-2

Solution for 2x+1=3/2x-2 equation:

2x+1=3/2x-2

We move all terms to the left:

2x+1-(3/2x-2)=0


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

x∈R


We get rid of parentheses

2x-3/2x+2+1=0

We multiply all the terms by the denominator


2x*2x+2*2x+1*2x-3=0

Wy multiply elements

4x^2+4x+2x-3=0

We add all the numbers together, and all the variables

4x^2+6x-3=0

a = 4; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·4·(-3)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*4}=\frac{-6-2\sqrt{21}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*4}=\frac{-6+2\sqrt{21}}{8}
$