1/2x-2=11/4x

Solution for 1/2x-2=11/4x equation:

1/2x-2=11/4x

We move all terms to the left:

1/2x-2-(11/4x)=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-(+11/4x)-2=0

We get rid of parentheses

1/2x-11/4x-2=0

We calculate fractions


4x/8x^2+(-22x)/8x^2-2=0

We multiply all the terms by the denominator


4x+(-22x)-2*8x^2=0

Wy multiply elements

-16x^2+4x+(-22x)=0

We get rid of parentheses

-16x^2+4x-22x=0

We add all the numbers together, and all the variables

-16x^2-18x=0

a = -16; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-16)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-16}=\frac{0}{-32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-16}=\frac{36}{-32}
=-1+1/8
$