1/2x-3/4=2/3x+2

Solution for 1/2x-3/4=2/3x+2 equation:

1/2x-3/4=2/3x+2

We move all terms to the left:

1/2x-3/4-(2/3x+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

1/2x-2/3x-2-3/4=0

We calculate fractions


(-54x^2)/96x^2+48x/96x^2+(-64x)/96x^2-2=0

We multiply all the terms by the denominator


(-54x^2)+48x+(-64x)-2*96x^2=0

Wy multiply elements

(-54x^2)-192x^2+48x+(-64x)=0

We get rid of parentheses

-54x^2-192x^2+48x-64x=0

We add all the numbers together, and all the variables

-246x^2-16x=0

a = -246; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-246)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-246}=\frac{0}{-492}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-246}=\frac{32}{-492}
=-8/123
$