Y=y(3y-21)

Solution for Y=y(3y-21) equation:

=Y(3Y-21)

We move all terms to the left:

-(Y(3Y-21))=0


We calculate terms in parentheses: -(Y(3Y-21)), so:

Y(3Y-21)

We multiply parentheses

3Y^2-21Y

Back to the equation:

-(3Y^2-21Y)


We get rid of parentheses

-3Y^2+21Y=0

a = -3; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-3)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-3}=\frac{-42}{-6}
=+7
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-3}=\frac{0}{-6}
=0
$