Y=6x(5x+2)

Solution for Y=6x(5x+2) equation:

=6Y(5Y+2)

We move all terms to the left:

-(6Y(5Y+2))=0


We calculate terms in parentheses: -(6Y(5Y+2)), so:

6Y(5Y+2)

We multiply parentheses

30Y^2+12Y

Back to the equation:

-(30Y^2+12Y)


We get rid of parentheses

-30Y^2-12Y=0

a = -30; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-30)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-30}=\frac{0}{-60}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-30}=\frac{24}{-60}
=-2/5
$