2x-3=3/2x+6

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

2x-3=3/2x+6

We move all terms to the left:

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


Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-12x-6x-3=0

We add all the numbers together, and all the variables

4x^2-18x-3=0

a = 4; b = -18; c = -3;
Δ = b2-4ac
Δ = -182-4·4·(-3)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*4}=\frac{18-2\sqrt{93}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*4}=\frac{18+2\sqrt{93}}{8}
$