(0.5/y)=(y+3)/8

Solution for (0.5/y)=(y+3)/8 equation:

(0.5/y)=(y+3)/8

We move all terms to the left:

(0.5/y)-((y+3)/8)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+0.5/y)-((y+3)/8)=0

We get rid of parentheses

0.5/y-((y+3)/8)=0

We calculate fractions


()/8y^2+(-((y+3)*y)/8y^2=0

We multiply all the terms by the denominator


(-((y+3)*y)+()=0


We calculate terms in parentheses: +(-((y+3)*y)+(), so:

-((y+3)*y)+(

We add all the numbers together, and all the variables

-((y+3)*y)


We calculate terms in parentheses: -((y+3)*y), so:

(y+3)*y

We multiply parentheses

y^2+3y

Back to the equation:

-(y^2+3y)


We get rid of parentheses

-y^2-3y

We add all the numbers together, and all the variables

-1y^2-3y

Back to the equation:

+(-1y^2-3y)


We get rid of parentheses

-1y^2-3y=0

a = -1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-1)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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