-3/2x-2=x+3

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

-3/2x-2=x+3

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2-10x-3=0

a = -2; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·(-2)·(-3)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{19}}{2*-2}=\frac{10-2\sqrt{19}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{19}}{2*-2}=\frac{10+2\sqrt{19}}{-4}
$