-1/4x+6=2/8x+28

Solution for -1/4x+6=2/8x+28 equation:

-1/4x+6=2/8x+28

We move all terms to the left:

-1/4x+6-(2/8x+28)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+28)!=0

x∈R


We get rid of parentheses

-1/4x-2/8x-28+6=0

We calculate fractions


(-8x)/32x^2+(-8x)/32x^2-28+6=0

We add all the numbers together, and all the variables

(-8x)/32x^2+(-8x)/32x^2-22=0

We multiply all the terms by the denominator


(-8x)+(-8x)-22*32x^2=0

Wy multiply elements

-704x^2+(-8x)+(-8x)=0

We get rid of parentheses

-704x^2-8x-8x=0

We add all the numbers together, and all the variables

-704x^2-16x=0

a = -704; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-704)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-704}=\frac{0}{-1408}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-704}=\frac{32}{-1408}
=-1/44
$