3/2x+3=x+1

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

3/2x+3=x+1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -2; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·(-2)·3
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{10}}{2*-2}=\frac{-4-2\sqrt{10}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{10}}{2*-2}=\frac{-4+2\sqrt{10}}{-4}
$