Y=x^2+3*x-9

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

=Y^2+3Y-9

We move all terms to the left:

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

We get rid of parentheses

-Y^2-3Y+9=0

We add all the numbers together, and all the variables

-1Y^2-3Y+9=0

a = -1; b = -3; c = +9;
Δ = b2-4ac
Δ = -32-4·(-1)·9
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{5}}{2*-1}=\frac{3-3\sqrt{5}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{5}}{2*-1}=\frac{3+3\sqrt{5}}{-2}
$