-3/2x+3/4=5/3x-2

Solution for -3/2x+3/4=5/3x-2 equation:

-3/2x+3/4=5/3x-2

We move all terms to the left:

-3/2x+3/4-(5/3x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

-3/2x-5/3x+2+3/4=0

We calculate fractions


54x^2/96x^2+(-144x)/96x^2+(-160x)/96x^2+2=0

We multiply all the terms by the denominator


54x^2+(-144x)+(-160x)+2*96x^2=0

Wy multiply elements

54x^2+192x^2+(-144x)+(-160x)=0

We get rid of parentheses

54x^2+192x^2-144x-160x=0

We add all the numbers together, and all the variables

246x^2-304x=0

a = 246; b = -304; c = 0;
Δ = b2-4ac
Δ = -3042-4·246·0
Δ = 92416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{92416}=304$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-304)-304}{2*246}=\frac{0}{492}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-304)+304}{2*246}=\frac{608}{492}
=1+29/123
$