Y=(3n-7)(7n+6)

Solution for Y=(3n-7)(7n+6) equation:

=(3Y-7)(7Y+6)

We move all terms to the left:

-((3Y-7)(7Y+6))=0

We multiply parentheses ..

-((+21Y^2+18Y-49Y-42))=0


We calculate terms in parentheses: -((+21Y^2+18Y-49Y-42)), so:

(+21Y^2+18Y-49Y-42)

We get rid of parentheses

21Y^2+18Y-49Y-42

We add all the numbers together, and all the variables

21Y^2-31Y-42

Back to the equation:

-(21Y^2-31Y-42)


We get rid of parentheses

-21Y^2+31Y+42=0

a = -21; b = 31; c = +42;
Δ = b2-4ac
Δ = 312-4·(-21)·42
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-67}{2*-21}=\frac{-98}{-42}
=2+1/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+67}{2*-21}=\frac{36}{-42}
=-6/7
$