Y=2(x-1)(x-6)

Solution for Y=2(x-1)(x-6) equation:

=2(Y-1)(Y-6)

We move all terms to the left:

-(2(Y-1)(Y-6))=0

We multiply parentheses ..

-(2(+Y^2-6Y-1Y+6))=0


We calculate terms in parentheses: -(2(+Y^2-6Y-1Y+6)), so:

2(+Y^2-6Y-1Y+6)

We multiply parentheses

2Y^2-12Y-2Y+12

We add all the numbers together, and all the variables

2Y^2-14Y+12

Back to the equation:

-(2Y^2-14Y+12)


We get rid of parentheses

-2Y^2+14Y-12=0

a = -2; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·(-2)·(-12)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*-2}=\frac{-24}{-4}
=+6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-2}=\frac{-4}{-4}
=1
$