Y=x2+9x+6

Solution for Y=x2+9x+6 equation:

=Y2+9Y+6

We move all terms to the left:

-(Y2+9Y+6)=0

We add all the numbers together, and all the variables

-(+Y^2+9Y+6)=0

We get rid of parentheses

-Y^2-9Y-6=0

We add all the numbers together, and all the variables

-1Y^2-9Y-6=0

a = -1; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·(-1)·(-6)
Δ = 57
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{-(-9)-\sqrt{57}}{2*-1}=\frac{9-\sqrt{57}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*-1}=\frac{9+\sqrt{57}}{-2}
$