Y=x(6x-36)

Solution for Y=x(6x-36) equation:

=Y(6Y-36)

We move all terms to the left:

-(Y(6Y-36))=0


We calculate terms in parentheses: -(Y(6Y-36)), so:

Y(6Y-36)

We multiply parentheses

6Y^2-36Y

Back to the equation:

-(6Y^2-36Y)


We get rid of parentheses

-6Y^2+36Y=0

a = -6; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-6)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-6}=\frac{-72}{-12}
=+6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-6}=\frac{0}{-12}
=0
$