y/6y-10y-11=8y-2y+29

Solution for y/6y-10y-11=8y-2y+29 equation:

y/6y-10y-11=8y-2y+29

We move all terms to the left:

y/6y-10y-11-(8y-2y+29)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

y/6y-10y-(6y+29)-11=0

We add all the numbers together, and all the variables

-10y+y/6y-(6y+29)-11=0

We get rid of parentheses

-10y+y/6y-6y-29-11=0

We multiply all the terms by the denominator


-10y*6y+y-6y*6y-29*6y-11*6y=0

We add all the numbers together, and all the variables

y-10y*6y-6y*6y-29*6y-11*6y=0

Wy multiply elements

-60y^2-36y^2+y-174y-66y=0

We add all the numbers together, and all the variables

-96y^2-239y=0

a = -96; b = -239; c = 0;
Δ = b2-4ac
Δ = -2392-4·(-96)·0
Δ = 57121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57121}=239$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-239)-239}{2*-96}=\frac{0}{-192}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-239)+239}{2*-96}=\frac{478}{-192}
=-2+47/96
$