Y=-2.5x^2-3x+9

Solution for Y=-2.5x^2-3x+9 equation:

=-2.5Y^2-3Y+9

We move all terms to the left:

-(-2.5Y^2-3Y+9)=0

We get rid of parentheses

2.5Y^2+3Y-9=0

a = 2.5; b = 3; c = -9;
Δ = b2-4ac
Δ = 32-4·2.5·(-9)
Δ = 99
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{99}=\sqrt{9*11}=\sqrt{9}*\sqrt{11}=3\sqrt{11}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{11}}{2*2.5}=\frac{-3-3\sqrt{11}}{5}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{11}}{2*2.5}=\frac{-3+3\sqrt{11}}{5}
$