Y=(2x+7)(3x-1)

Solution for Y=(2x+7)(3x-1) equation:

=(2Y+7)(3Y-1)

We move all terms to the left:

-((2Y+7)(3Y-1))=0

We multiply parentheses ..

-((+6Y^2-2Y+21Y-7))=0


We calculate terms in parentheses: -((+6Y^2-2Y+21Y-7)), so:

(+6Y^2-2Y+21Y-7)

We get rid of parentheses

6Y^2-2Y+21Y-7

We add all the numbers together, and all the variables

6Y^2+19Y-7

Back to the equation:

-(6Y^2+19Y-7)


We get rid of parentheses

-6Y^2-19Y+7=0

a = -6; b = -19; c = +7;
Δ = b2-4ac
Δ = -192-4·(-6)·7
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-23}{2*-6}=\frac{-4}{-12}
=1/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+23}{2*-6}=\frac{42}{-12}
=-3+1/2
$