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

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

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

We move all terms to the left:

-1/4y+6-(2/3y+28)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



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

y∈R


We get rid of parentheses

-1/4y-2/3y-28+6=0

We calculate fractions


(-3y)/12y^2+(-8y)/12y^2-28+6=0

We add all the numbers together, and all the variables

(-3y)/12y^2+(-8y)/12y^2-22=0

We multiply all the terms by the denominator


(-3y)+(-8y)-22*12y^2=0

Wy multiply elements

-264y^2+(-3y)+(-8y)=0

We get rid of parentheses

-264y^2-3y-8y=0

We add all the numbers together, and all the variables

-264y^2-11y=0

a = -264; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-264)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-264}=\frac{0}{-528}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-264}=\frac{22}{-528}
=-1/24
$