Y=3x(x+7)

Solution for Y=3x(x+7) equation:

=3Y(Y+7)

We move all terms to the left:

-(3Y(Y+7))=0


We calculate terms in parentheses: -(3Y(Y+7)), so:

3Y(Y+7)

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