Y=(3x+12)(x-7)

Solution for Y=(3x+12)(x-7) equation:

=(3Y+12)(Y-7)

We move all terms to the left:

-((3Y+12)(Y-7))=0

We multiply parentheses ..

-((+3Y^2-21Y+12Y-84))=0


We calculate terms in parentheses: -((+3Y^2-21Y+12Y-84)), so:

(+3Y^2-21Y+12Y-84)

We get rid of parentheses

3Y^2-21Y+12Y-84

We add all the numbers together, and all the variables

3Y^2-9Y-84

Back to the equation:

-(3Y^2-9Y-84)


We get rid of parentheses

-3Y^2+9Y+84=0

a = -3; b = 9; c = +84;
Δ = b2-4ac
Δ = 92-4·(-3)·84
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-33}{2*-3}=\frac{-42}{-6}
=+7
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+33}{2*-3}=\frac{24}{-6}
=-4
$