5-1/2x=2/8x+2

Solution for 5-1/2x=2/8x+2 equation:

5-1/2x=2/8x+2

We move all terms to the left:

5-1/2x-(2/8x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+2)!=0

x∈R


We get rid of parentheses

-1/2x-2/8x-2+5=0

We calculate fractions


(-8x)/16x^2+(-4x)/16x^2-2+5=0

We add all the numbers together, and all the variables

(-8x)/16x^2+(-4x)/16x^2+3=0

We multiply all the terms by the denominator


(-8x)+(-4x)+3*16x^2=0

Wy multiply elements

48x^2+(-8x)+(-4x)=0

We get rid of parentheses

48x^2-8x-4x=0

We add all the numbers together, and all the variables

48x^2-12x=0

a = 48; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·48·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*48}=\frac{0}{96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*48}=\frac{24}{96}
=1/4
$