Y=(8x+5)(8x-2)

Solution for Y=(8x+5)(8x-2) equation:

=(8Y+5)(8Y-2)

We move all terms to the left:

-((8Y+5)(8Y-2))=0

We multiply parentheses ..

-((+64Y^2-16Y+40Y-10))=0


We calculate terms in parentheses: -((+64Y^2-16Y+40Y-10)), so:

(+64Y^2-16Y+40Y-10)

We get rid of parentheses

64Y^2-16Y+40Y-10

We add all the numbers together, and all the variables

64Y^2+24Y-10

Back to the equation:

-(64Y^2+24Y-10)


We get rid of parentheses

-64Y^2-24Y+10=0

a = -64; b = -24; c = +10;
Δ = b2-4ac
Δ = -242-4·(-64)·10
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-56}{2*-64}=\frac{-32}{-128}
=1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+56}{2*-64}=\frac{80}{-128}
=-5/8
$