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

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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} $

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