3(y-5)=5y(3-y)

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

3(y-5)=5y(3-y)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3y-(5y(-1y+3))-15=0


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

5y(-1y+3)

We multiply parentheses

-5y^2+15y

Back to the equation:

-(-5y^2+15y)


We get rid of parentheses

5y^2-15y+3y-15=0

We add all the numbers together, and all the variables

5y^2-12y-15=0

a = 5; b = -12; c = -15;
Δ = b2-4ac
Δ = -122-4·5·(-15)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{111}}{2*5}=\frac{12-2\sqrt{111}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{111}}{2*5}=\frac{12+2\sqrt{111}}{10}
$