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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-((-1Y+3)(3Y-7))=0

We multiply parentheses ..

-((-3Y^2+7Y+9Y-21))=0


We calculate terms in parentheses: -((-3Y^2+7Y+9Y-21)), so:

(-3Y^2+7Y+9Y-21)

We get rid of parentheses

-3Y^2+7Y+9Y-21

We add all the numbers together, and all the variables

-3Y^2+16Y-21

Back to the equation:

-(-3Y^2+16Y-21)


We get rid of parentheses

3Y^2-16Y+21=0

a = 3; b = -16; c = +21;
Δ = b2-4ac
Δ = -162-4·3·21
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2}{2*3}=\frac{14}{6}
=2+1/3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2}{2*3}=\frac{18}{6}
=3
$