Y=(3x+15)(x-2)

Solution for Y=(3x+15)(x-2) equation:

=(3Y+15)(Y-2)

We move all terms to the left:

-((3Y+15)(Y-2))=0

We multiply parentheses ..

-((+3Y^2-6Y+15Y-30))=0


We calculate terms in parentheses: -((+3Y^2-6Y+15Y-30)), so:

(+3Y^2-6Y+15Y-30)

We get rid of parentheses

3Y^2-6Y+15Y-30

We add all the numbers together, and all the variables

3Y^2+9Y-30

Back to the equation:

-(3Y^2+9Y-30)


We get rid of parentheses

-3Y^2-9Y+30=0

a = -3; b = -9; c = +30;
Δ = b2-4ac
Δ = -92-4·(-3)·30
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{-(-9)-21}{2*-3}=\frac{-12}{-6}
=+2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+21}{2*-3}=\frac{30}{-6}
=-5
$