Y=x2+6x-19

Solution for Y=x2+6x-19 equation:

=Y2+6Y-19

We move all terms to the left:

-(Y2+6Y-19)=0

We add all the numbers together, and all the variables

-(+Y^2+6Y-19)=0

We get rid of parentheses

-Y^2-6Y+19=0

We add all the numbers together, and all the variables

-1Y^2-6Y+19=0

a = -1; b = -6; c = +19;
Δ = b2-4ac
Δ = -62-4·(-1)·19
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{7}}{2*-1}=\frac{6-4\sqrt{7}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{7}}{2*-1}=\frac{6+4\sqrt{7}}{-2}
$