Y=(2x-3)(6x+8)

Solution for Y=(2x-3)(6x+8) equation:

=(2Y-3)(6Y+8)

We move all terms to the left:

-((2Y-3)(6Y+8))=0

We multiply parentheses ..

-((+12Y^2+16Y-18Y-24))=0


We calculate terms in parentheses: -((+12Y^2+16Y-18Y-24)), so:

(+12Y^2+16Y-18Y-24)

We get rid of parentheses

12Y^2+16Y-18Y-24

We add all the numbers together, and all the variables

12Y^2-2Y-24

Back to the equation:

-(12Y^2-2Y-24)


We get rid of parentheses

-12Y^2+2Y+24=0

a = -12; b = 2; c = +24;
Δ = b2-4ac
Δ = 22-4·(-12)·24
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-34}{2*-12}=\frac{-36}{-24}
=1+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+34}{2*-12}=\frac{32}{-24}
=-1+1/3
$