3/2x+3=5x+1-x

Solution for 3/2x+3=5x+1-x equation:

3/2x+3=5x+1-x

We move all terms to the left:

3/2x+3-(5x+1-x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2-2x+6x+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}
$