Y=(3p-2)(7p-7)

Solution for Y=(3p-2)(7p-7) equation:

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

We move all terms to the left:

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

We multiply parentheses ..

-((+21Y^2-21Y-14Y+14))=0


We calculate terms in parentheses: -((+21Y^2-21Y-14Y+14)), so:

(+21Y^2-21Y-14Y+14)

We get rid of parentheses

21Y^2-21Y-14Y+14

We add all the numbers together, and all the variables

21Y^2-35Y+14

Back to the equation:

-(21Y^2-35Y+14)


We get rid of parentheses

-21Y^2+35Y-14=0

a = -21; b = 35; c = -14;
Δ = b2-4ac
Δ = 352-4·(-21)·(-14)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-7}{2*-21}=\frac{-42}{-42}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+7}{2*-21}=\frac{-28}{-42}
=2/3
$