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

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

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

We move all terms to the left:

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


Domain of the equation: 3)y!=0

y!=0/1

y!=0

y∈R


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

We add all the numbers together, and all the variables

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

We multiply parentheses

2y^2-5-(+2/5)=0

We get rid of parentheses

2y^2-5-2/5=0

We multiply all the terms by the denominator


2y^2*5-2-5*5=0

We add all the numbers together, and all the variables

2y^2*5-27=0

Wy multiply elements

10y^2-27=0

a = 10; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·10·(-27)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{30}}{2*10}=\frac{0-6\sqrt{30}}{20}
=-\frac{6\sqrt{30}}{20}
=-\frac{3\sqrt{30}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{30}}{2*10}=\frac{0+6\sqrt{30}}{20}
=\frac{6\sqrt{30}}{20}
=\frac{3\sqrt{30}}{10}
$