3/2x+1=x+4

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

3/2x+1=x+4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2-6x+3=0

a = -2; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·(-2)·3
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*-2}=\frac{6-2\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*-2}=\frac{6+2\sqrt{15}}{-4}
$