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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-((-2Y+7)(-1Y+8))=0

We multiply parentheses ..

-((+2Y^2-16Y-7Y+56))=0


We calculate terms in parentheses: -((+2Y^2-16Y-7Y+56)), so:

(+2Y^2-16Y-7Y+56)

We get rid of parentheses

2Y^2-16Y-7Y+56

We add all the numbers together, and all the variables

2Y^2-23Y+56

Back to the equation:

-(2Y^2-23Y+56)


We get rid of parentheses

-2Y^2+23Y-56=0

a = -2; b = 23; c = -56;
Δ = b2-4ac
Δ = 232-4·(-2)·(-56)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-9}{2*-2}=\frac{-32}{-4}
=+8
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+9}{2*-2}=\frac{-14}{-4}
=3+1/2
$