X=3y(2+5y)

Solution for X=3y(2+5y) equation:

X=3X(2+5X)

We move all terms to the left:

X-(3X(2+5X))=0

We add all the numbers together, and all the variables

X-(3X(5X+2))=0


We calculate terms in parentheses: -(3X(5X+2)), so:

3X(5X+2)

We multiply parentheses

15X^2+6X

Back to the equation:

-(15X^2+6X)


We get rid of parentheses

-15X^2+X-6X=0

We add all the numbers together, and all the variables

-15X^2-5X=0

a = -15; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-15)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-15}=\frac{0}{-30}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-15}=\frac{10}{-30}
=-1/3
$