3/2)(2x+6)=3x+9

Solution for 3/2)(2x+6)=3x+9 equation:

3/2)(2x+6)=3x+9

We move all terms to the left:

3/2)(2x+6)-(3x+9)=0


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

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-6x^2+9=0

a = -6; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-6)·9
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*-6}=\frac{0-6\sqrt{6}}{-12}
=-\frac{6\sqrt{6}}{-12}
=-\frac{\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*-6}=\frac{0+6\sqrt{6}}{-12}
=\frac{6\sqrt{6}}{-12}
=\frac{\sqrt{6}}{-2}
$