-1/4x+6=6-2/3x+28

Solution for -1/4x+6=6-2/3x+28 equation:

-1/4x+6=6-2/3x+28

We move all terms to the left:

-1/4x+6-(6-2/3x+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 add all the numbers together, and all the variables

-1/4x-(-2/3x+34)+6=0

We get rid of parentheses

-1/4x+2/3x-34+6=0

We calculate fractions


(-3x)/12x^2+8x/12x^2-34+6=0

We add all the numbers together, and all the variables

(-3x)/12x^2+8x/12x^2-28=0

We multiply all the terms by the denominator


(-3x)+8x-28*12x^2=0

We add all the numbers together, and all the variables

8x+(-3x)-28*12x^2=0

Wy multiply elements

-336x^2+8x+(-3x)=0

We get rid of parentheses

-336x^2+8x-3x=0

We add all the numbers together, and all the variables

-336x^2+5x=0

a = -336; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-336)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-336}=\frac{-10}{-672}
=5/336
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-336}=\frac{0}{-672}
=0
$