Y=0.9(x-4)(x-3)

Solution for Y=0.9(x-4)(x-3) equation:

=0.9(Y-4)(Y-3)

We move all terms to the left:

-(0.9(Y-4)(Y-3))=0

We multiply parentheses ..

-(0.9(+Y^2-3Y-4Y+12))=0


We calculate terms in parentheses: -(0.9(+Y^2-3Y-4Y+12)), so:

0.9(+Y^2-3Y-4Y+12)

We multiply parentheses

0.9Y^2-2.7Y-3.6Y+10.8

We add all the numbers together, and all the variables

0.9Y^2-6.3Y+10.8

Back to the equation:

-(0.9Y^2-6.3Y+10.8)


We get rid of parentheses

-0.9Y^2+6.3Y-10.8=0

a = -0.9; b = 6.3; c = -10.8;
Δ = b2-4ac
Δ = 6.32-4·(-0.9)·(-10.8)
Δ = 0.81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6.3)-\sqrt{0.81}}{2*-0.9}=\frac{-6.3-\sqrt{0.81}}{-1.8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.3)+\sqrt{0.81}}{2*-0.9}=\frac{-6.3+\sqrt{0.81}}{-1.8}
$