(3/10)y=31/3

Solution for (3/10)y=31/3 equation:

(3/10)y=31/3

We move all terms to the left:

(3/10)y-(31/3)=0


Domain of the equation: 10)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+3/10)y-(+31/3)=0

We multiply parentheses

3y^2-(+31/3)=0

We get rid of parentheses

3y^2-31/3=0

We multiply all the terms by the denominator


3y^2*3-31=0

Wy multiply elements

9y^2-31=0

a = 9; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·9·(-31)
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{31}}{2*9}=\frac{0-6\sqrt{31}}{18}
=-\frac{6\sqrt{31}}{18}
=-\frac{\sqrt{31}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{31}}{2*9}=\frac{0+6\sqrt{31}}{18}
=\frac{6\sqrt{31}}{18}
=\frac{\sqrt{31}}{3}
$