Y=(7x-1)(6x-1)

Solution for Y=(7x-1)(6x-1) equation:

=(7Y-1)(6Y-1)

We move all terms to the left:

-((7Y-1)(6Y-1))=0

We multiply parentheses ..

-((+42Y^2-7Y-6Y+1))=0


We calculate terms in parentheses: -((+42Y^2-7Y-6Y+1)), so:

(+42Y^2-7Y-6Y+1)

We get rid of parentheses

42Y^2-7Y-6Y+1

We add all the numbers together, and all the variables

42Y^2-13Y+1

Back to the equation:

-(42Y^2-13Y+1)


We get rid of parentheses

-42Y^2+13Y-1=0

a = -42; b = 13; c = -1;
Δ = b2-4ac
Δ = 132-4·(-42)·(-1)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-1}{2*-42}=\frac{-14}{-84}
=1/6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+1}{2*-42}=\frac{-12}{-84}
=1/7
$