Y=(1,5x+4)(12-6x)

Solution for Y=(1,5x+4)(12-6x) equation:

=(1.5Y+4)(12-6Y)

We move all terms to the left:

-((1.5Y+4)(12-6Y))=0

We add all the numbers together, and all the variables

-((1.5Y+4)(-6Y+12))=0

We multiply parentheses ..

-((-6Y^2+12Y-24Y+48))=0


We calculate terms in parentheses: -((-6Y^2+12Y-24Y+48)), so:

(-6Y^2+12Y-24Y+48)

We get rid of parentheses

-6Y^2+12Y-24Y+48

We add all the numbers together, and all the variables

-6Y^2-12Y+48

Back to the equation:

-(-6Y^2-12Y+48)


We get rid of parentheses

6Y^2+12Y-48=0

a = 6; b = 12; c = -48;
Δ = b2-4ac
Δ = 122-4·6·(-48)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-36}{2*6}=\frac{-48}{12}
=-4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+36}{2*6}=\frac{24}{12}
=2
$