2x-6=3/2x+1

Solution for 2x-6=3/2x+1 equation:

2x-6=3/2x+1

We move all terms to the left:

2x-6-(3/2x+1)=0


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

x∈R


We get rid of parentheses

2x-3/2x-1-6=0

We multiply all the terms by the denominator


2x*2x-1*2x-6*2x-3=0

Wy multiply elements

4x^2-2x-12x-3=0

We add all the numbers together, and all the variables

4x^2-14x-3=0

a = 4; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·4·(-3)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{61}}{2*4}=\frac{14-2\sqrt{61}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{61}}{2*4}=\frac{14+2\sqrt{61}}{8}
$