3/2x+2=-4+3x

Solution for 3/2x+2=-4+3x equation:

3/2x+2=-4+3x

We move all terms to the left:

3/2x+2-(-4+3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(3x-4)+2=0

We get rid of parentheses

3/2x-3x+4+2=0

We multiply all the terms by the denominator


-3x*2x+4*2x+2*2x+3=0

Wy multiply elements

-6x^2+8x+4x+3=0

We add all the numbers together, and all the variables

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

a = -6; b = 12; c = +3;
Δ = b2-4ac
Δ = 122-4·(-6)·3
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{-(12)-6\sqrt{6}}{2*-6}=\frac{-12-6\sqrt{6}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{6}}{2*-6}=\frac{-12+6\sqrt{6}}{-12}
$