Y=-1.179(x^2-12x+36)+42

Solution for Y=-1.179(x^2-12x+36)+42 equation:

=-1.179(Y^2-12Y+36)+42

We move all terms to the left:

-(-1.179(Y^2-12Y+36)+42)=0


We calculate terms in parentheses: -(-1.179(Y^2-12Y+36)+42), so:

-1.179(Y^2-12Y+36)+42

We multiply parentheses

-1.179Y^2+14.148Y-42.444+42

We add all the numbers together, and all the variables

-1.179Y^2+14.148Y-0.444

Back to the equation:

-(-1.179Y^2+14.148Y-0.444)


We get rid of parentheses

1.179Y^2-14.148Y+0.444=0

a = 1.179; b = -14.148; c = +0.444;
Δ = b2-4ac
Δ = -14.1482-4·1.179·0.444
Δ = 198.072
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{-(-14.148)-\sqrt{198.072}}{2*1.179}=\frac{14.148-\sqrt{198.072}}{2.358}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14.148)+\sqrt{198.072}}{2*1.179}=\frac{14.148+\sqrt{198.072}}{2.358}
$