Y=(8x-1)(2x-3)

Solution for Y=(8x-1)(2x-3) equation:

=(8Y-1)(2Y-3)

We move all terms to the left:

-((8Y-1)(2Y-3))=0

We multiply parentheses ..

-((+16Y^2-24Y-2Y+3))=0


We calculate terms in parentheses: -((+16Y^2-24Y-2Y+3)), so:

(+16Y^2-24Y-2Y+3)

We get rid of parentheses

16Y^2-24Y-2Y+3

We add all the numbers together, and all the variables

16Y^2-26Y+3

Back to the equation:

-(16Y^2-26Y+3)


We get rid of parentheses

-16Y^2+26Y-3=0

a = -16; b = 26; c = -3;
Δ = b2-4ac
Δ = 262-4·(-16)·(-3)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-22}{2*-16}=\frac{-48}{-32}
=1+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+22}{2*-16}=\frac{-4}{-32}
=1/8
$