Y=(2x+7)(3x-8)

Solution for Y=(2x+7)(3x-8) equation:

=(2Y+7)(3Y-8)

We move all terms to the left:

-((2Y+7)(3Y-8))=0

We multiply parentheses ..

-((+6Y^2-16Y+21Y-56))=0


We calculate terms in parentheses: -((+6Y^2-16Y+21Y-56)), so:

(+6Y^2-16Y+21Y-56)

We get rid of parentheses

6Y^2-16Y+21Y-56

We add all the numbers together, and all the variables

6Y^2+5Y-56

Back to the equation:

-(6Y^2+5Y-56)


We get rid of parentheses

-6Y^2-5Y+56=0

a = -6; b = -5; c = +56;
Δ = b2-4ac
Δ = -52-4·(-6)·56
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-37}{2*-6}=\frac{-32}{-12}
=2+2/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+37}{2*-6}=\frac{42}{-12}
=-3+1/2
$