3x-3=3/2x+9

Solution for 3x-3=3/2x+9 equation:

3x-3=3/2x+9

We move all terms to the left:

3x-3-(3/2x+9)=0


Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

3x-3/2x-9-3=0

We multiply all the terms by the denominator


3x*2x-9*2x-3*2x-3=0

Wy multiply elements

6x^2-18x-6x-3=0

We add all the numbers together, and all the variables

6x^2-24x-3=0

a = 6; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·6·(-3)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18\sqrt{2}}{2*6}=\frac{24-18\sqrt{2}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18\sqrt{2}}{2*6}=\frac{24+18\sqrt{2}}{12}
$