(5/2)y=(y+5)

Solution for (5/2)y=(y+5) equation:

(5/2)y=(y+5)

We move all terms to the left:

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


Domain of the equation: 2)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -((y+5)), so:

(y+5)

We get rid of parentheses

y+5

Back to the equation:

-(y+5)


We get rid of parentheses

5y^2-y-5=0

We add all the numbers together, and all the variables

5y^2-1y-5=0

a = 5; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·5·(-5)
Δ = 101
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{101}}{2*5}=\frac{1-\sqrt{101}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{101}}{2*5}=\frac{1+\sqrt{101}}{10}
$