x-3=3/2x+1

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

x-3=3/2x+1

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

a = 2; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·2·(-3)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{22}}{2*2}=\frac{8-2\sqrt{22}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{22}}{2*2}=\frac{8+2\sqrt{22}}{4}
$