4x-1=3/2x+1

Solution for 4x-1=3/2x+1 equation:

4x-1=3/2x+1

We move all terms to the left:

4x-1-(3/2x+1)=0


Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

4x-3/2x-1-1=0

We multiply all the terms by the denominator


4x*2x-1*2x-1*2x-3=0

Wy multiply elements

8x^2-2x-2x-3=0

We add all the numbers together, and all the variables

8x^2-4x-3=0

a = 8; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·8·(-3)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*8}=\frac{4-4\sqrt{7}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*8}=\frac{4+4\sqrt{7}}{16}
$