Y=(4x-7)(6x+5)

Solution for Y=(4x-7)(6x+5) equation:

=(4Y-7)(6Y+5)

We move all terms to the left:

-((4Y-7)(6Y+5))=0

We multiply parentheses ..

-((+24Y^2+20Y-42Y-35))=0


We calculate terms in parentheses: -((+24Y^2+20Y-42Y-35)), so:

(+24Y^2+20Y-42Y-35)

We get rid of parentheses

24Y^2+20Y-42Y-35

We add all the numbers together, and all the variables

24Y^2-22Y-35

Back to the equation:

-(24Y^2-22Y-35)


We get rid of parentheses

-24Y^2+22Y+35=0

a = -24; b = 22; c = +35;
Δ = b2-4ac
Δ = 222-4·(-24)·35
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-62}{2*-24}=\frac{-84}{-48}
=1+3/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+62}{2*-24}=\frac{40}{-48}
=-5/6
$