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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

8x^2-10x-3=0

a = 8; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·8·(-3)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*8}=\frac{-4}{16}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*8}=\frac{24}{16}
=1+1/2
$