Y=x2+6x-16

Solution for Y=x2+6x-16 equation:

=Y2+6Y-16

We move all terms to the left:

-(Y2+6Y-16)=0

We add all the numbers together, and all the variables

-(+Y^2+6Y-16)=0

We get rid of parentheses

-Y^2-6Y+16=0

We add all the numbers together, and all the variables

-1Y^2-6Y+16=0

a = -1; b = -6; c = +16;
Δ = b2-4ac
Δ = -62-4·(-1)·16
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*-1}=\frac{-4}{-2}
=+2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*-1}=\frac{16}{-2}
=-8
$