3=5y(8+1/5y)

Solution for 3=5y(8+1/5y) equation:

3=5y(8+1/5y)

We move all terms to the left:

3-(5y(8+1/5y))=0


Domain of the equation: 5y))!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-(5y(1/5y+8))+3=0

We multiply all the terms by the denominator


-(5y(1+3*5y+8))=0


We calculate terms in parentheses: -(5y(1+3*5y+8)), so:

5y(1+3*5y+8)

We add all the numbers together, and all the variables

5y(3*5y+9)

We multiply parentheses

75y^2+45y

Back to the equation:

-(75y^2+45y)


We get rid of parentheses

-75y^2-45y=0

a = -75; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·(-75)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*-75}=\frac{0}{-150}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*-75}=\frac{90}{-150}
=-3/5
$