Y=(6x+4)(7x-8)

Solution for Y=(6x+4)(7x-8) equation:

=(6Y+4)(7Y-8)

We move all terms to the left:

-((6Y+4)(7Y-8))=0

We multiply parentheses ..

-((+42Y^2-48Y+28Y-32))=0


We calculate terms in parentheses: -((+42Y^2-48Y+28Y-32)), so:

(+42Y^2-48Y+28Y-32)

We get rid of parentheses

42Y^2-48Y+28Y-32

We add all the numbers together, and all the variables

42Y^2-20Y-32

Back to the equation:

-(42Y^2-20Y-32)


We get rid of parentheses

-42Y^2+20Y+32=0

a = -42; b = 20; c = +32;
Δ = b2-4ac
Δ = 202-4·(-42)·32
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-76}{2*-42}=\frac{-96}{-84}
=1+1/7
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+76}{2*-42}=\frac{56}{-84}
=-2/3
$