-1/2x+3=41/4x

Solution for -1/2x+3=41/4x equation:

-1/2x+3=41/4x

We move all terms to the left:

-1/2x+3-(41/4x)=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-(+41/4x)+3=0

We get rid of parentheses

-1/2x-41/4x+3=0

We calculate fractions


(-4x)/8x^2+(-82x)/8x^2+3=0

We multiply all the terms by the denominator


(-4x)+(-82x)+3*8x^2=0

Wy multiply elements

24x^2+(-4x)+(-82x)=0

We get rid of parentheses

24x^2-4x-82x=0

We add all the numbers together, and all the variables

24x^2-86x=0

a = 24; b = -86; c = 0;
Δ = b2-4ac
Δ = -862-4·24·0
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-86}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+86}{2*24}=\frac{172}{48}
=3+7/12
$