3(x+3)=3/2x+2

Solution for 3(x+3)=3/2x+2 equation:

3(x+3)=3/2x+2

We move all terms to the left:

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


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

x∈R


We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-4x+18x-3=0

We add all the numbers together, and all the variables

6x^2+14x-3=0

a = 6; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·6·(-3)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{67}}{2*6}=\frac{-14-2\sqrt{67}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{67}}{2*6}=\frac{-14+2\sqrt{67}}{12}
$