31/3y+4=16y=

Solution for 31/3y+4=16y= equation:

31/3y+4=16y=

We move all terms to the left:

31/3y+4-(16y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-16y+31/3y+4=0

We multiply all the terms by the denominator


-16y*3y+4*3y+31=0

Wy multiply elements

-48y^2+12y+31=0

a = -48; b = 12; c = +31;
Δ = b2-4ac
Δ = 122-4·(-48)·31
Δ = 6096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6096}=\sqrt{16*381}=\sqrt{16}*\sqrt{381}=4\sqrt{381}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{381}}{2*-48}=\frac{-12-4\sqrt{381}}{-96}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{381}}{2*-48}=\frac{-12+4\sqrt{381}}{-96}
$