1/2x-3=23/4x

Solution for 1/2x-3=23/4x equation:

1/2x-3=23/4x

We move all terms to the left:

1/2x-3-(23/4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+23/4x)-3=0

We get rid of parentheses

1/2x-23/4x-3=0

We calculate fractions


4x/8x^2+(-46x)/8x^2-3=0

We multiply all the terms by the denominator


4x+(-46x)-3*8x^2=0

Wy multiply elements

-24x^2+4x+(-46x)=0

We get rid of parentheses

-24x^2+4x-46x=0

We add all the numbers together, and all the variables

-24x^2-42x=0

a = -24; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·(-24)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*-24}=\frac{84}{-48}
=-1+3/4
$