y/6y-28=4y+10

Solution for y/6y-28=4y+10 equation:

y/6y-28=4y+10

We move all terms to the left:

y/6y-28-(4y+10)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We get rid of parentheses

y/6y-4y-10-28=0

We multiply all the terms by the denominator


y-4y*6y-10*6y-28*6y=0

Wy multiply elements

-24y^2+y-60y-168y=0

We add all the numbers together, and all the variables

-24y^2-227y=0

a = -24; b = -227; c = 0;
Δ = b2-4ac
Δ = -2272-4·(-24)·0
Δ = 51529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{51529}=227$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-227)-227}{2*-24}=\frac{0}{-48}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-227)+227}{2*-24}=\frac{454}{-48}
=-9+11/24
$