6-1/4x=8+1/2x

Solution for 6-1/4x=8+1/2x equation:

6-1/4x=8+1/2x

We move all terms to the left:

6-1/4x-(8+1/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/4x-(1/2x+8)+6=0

We get rid of parentheses

-1/4x-1/2x-8+6=0

We calculate fractions


(-2x)/8x^2+(-4x)/8x^2-8+6=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-16x^2-6x=0

a = -16; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-16)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-16}=\frac{0}{-32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-16}=\frac{12}{-32}
=-3/8
$