(1/5)y-(2/3)=6

Solution for (1/5)y-(2/3)=6 equation:

(1/5)y-(2/3)=6

We move all terms to the left:

(1/5)y-(2/3)-(6)=0


Domain of the equation: 5)y!=0

y!=0/1

y!=0

y∈R


determiningTheFunctionDomain
(1/5)y-6-(2/3)=0

We add all the numbers together, and all the variables

(+1/5)y-6-(+2/3)=0

We multiply parentheses

y^2-6-(+2/3)=0

We get rid of parentheses

y^2-6-2/3=0

We multiply all the terms by the denominator


y^2*3-2-6*3=0

We add all the numbers together, and all the variables

y^2*3-20=0

Wy multiply elements

3y^2-20=0

a = 3; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·3·(-20)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*3}=\frac{0-4\sqrt{15}}{6}
=-\frac{4\sqrt{15}}{6}
=-\frac{2\sqrt{15}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*3}=\frac{0+4\sqrt{15}}{6}
=\frac{4\sqrt{15}}{6}
=\frac{2\sqrt{15}}{3}
$