-1/4x+6=1/3x+28

Solution for -1/4x+6=1/3x+28 equation:

-1/4x+6=1/3x+28

We move all terms to the left:

-1/4x+6-(1/3x+28)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+28)!=0

x∈R


We get rid of parentheses

-1/4x-1/3x-28+6=0

We calculate fractions


(-3x)/12x^2+(-4x)/12x^2-28+6=0

We add all the numbers together, and all the variables

(-3x)/12x^2+(-4x)/12x^2-22=0

We multiply all the terms by the denominator


(-3x)+(-4x)-22*12x^2=0

Wy multiply elements

-264x^2+(-3x)+(-4x)=0

We get rid of parentheses

-264x^2-3x-4x=0

We add all the numbers together, and all the variables

-264x^2-7x=0

a = -264; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-264)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-264}=\frac{0}{-528}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-264}=\frac{14}{-528}
=-7/264
$