3/2x=2x-1

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

3/2x=2x-1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-2x+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -4; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-4)·3
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{13}}{2*-4}=\frac{-2-2\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{13}}{2*-4}=\frac{-2+2\sqrt{13}}{-8}
$