3/2x+1=2x+4

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

3/2x+1=2x+4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-8x+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}
$