(31/3)y+4=16

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

(31/3)y+4=16

We move all terms to the left:

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


Domain of the equation: 3)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

(+31/3)y-12=0

We multiply parentheses

31y^2-12=0

a = 31; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·31·(-12)
Δ = 1488
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:

$\sqrt{\Delta}=\sqrt{1488}=\sqrt{16*93}=\sqrt{16}*\sqrt{93}=4\sqrt{93}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{93}}{2*31}=\frac{0-4\sqrt{93}}{62}
=-\frac{4\sqrt{93}}{62}
=-\frac{2\sqrt{93}}{31}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{93}}{2*31}=\frac{0+4\sqrt{93}}{62}
=\frac{4\sqrt{93}}{62}
=\frac{2\sqrt{93}}{31}
$