31/4+1/2y+11/3+5/6y=511/12

Solution for 31/4+1/2y+11/3+5/6y=511/12 equation:

31/4+1/2y+11/3+5/6y=511/12

We move all terms to the left:

31/4+1/2y+11/3+5/6y-(511/12)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y+5/6y+31/4+11/3-(+511/12)=0

We get rid of parentheses

1/2y+5/6y+31/4+11/3-511/12=0

We calculate fractions


(-441504y^2)/6912y^2+80352y^2/6912y^2+38016y^2/6912y^2+3456y/6912y^2+5760y/6912y^2=0

We multiply all the terms by the denominator


(-441504y^2)+80352y^2+38016y^2+3456y+5760y=0

We add all the numbers together, and all the variables

118368y^2+(-441504y^2)+9216y=0

We get rid of parentheses

118368y^2-441504y^2+9216y=0

We add all the numbers together, and all the variables

-323136y^2+9216y=0

a = -323136; b = 9216; c = 0;
Δ = b2-4ac
Δ = 92162-4·(-323136)·0
Δ = 84934656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{84934656}=9216$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9216)-9216}{2*-323136}=\frac{-18432}{-646272}
=16/561
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9216)+9216}{2*-323136}=\frac{0}{-646272}
=0
$