-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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-264y^2+5y=0

a = -264; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-264)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-264}=\frac{-10}{-528}
=5/264
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-264}=\frac{0}{-528}
=0
$