21/2x+0.5=6.5+41/4x

Solution for 21/2x+0.5=6.5+41/4x equation:

21/2x+0.5=6.5+41/4x

We move all terms to the left:

21/2x+0.5-(6.5+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

21/2x-(41/4x+6.5)+0.5=0

We get rid of parentheses

21/2x-41/4x-6.5+0.5=0

We calculate fractions


84x/8x^2+(-82x)/8x^2-6.5+0.5=0

We add all the numbers together, and all the variables

84x/8x^2+(-82x)/8x^2-6=0

We multiply all the terms by the denominator


84x+(-82x)-6*8x^2=0

Wy multiply elements

-48x^2+84x+(-82x)=0

We get rid of parentheses

-48x^2+84x-82x=0

We add all the numbers together, and all the variables

-48x^2+2x=0

a = -48; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-48)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-48}=\frac{-4}{-96}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-48}=\frac{0}{-96}
=0
$