Y=x^2+12x-19

Solution for Y=x^2+12x-19 equation:

=Y^2+12Y-19

We move all terms to the left:

-(Y^2+12Y-19)=0

We get rid of parentheses

-Y^2-12Y+19=0

We add all the numbers together, and all the variables

-1Y^2-12Y+19=0

a = -1; b = -12; c = +19;
Δ = b2-4ac
Δ = -122-4·(-1)·19
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{55}}{2*-1}=\frac{12-2\sqrt{55}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{55}}{2*-1}=\frac{12+2\sqrt{55}}{-2}
$