Y=x^2+19x-36

Solution for Y=x^2+19x-36 equation:

=Y^2+19Y-36

We move all terms to the left:

-(Y^2+19Y-36)=0

We get rid of parentheses

-Y^2-19Y+36=0

We add all the numbers together, and all the variables

-1Y^2-19Y+36=0

a = -1; b = -19; c = +36;
Δ = b2-4ac
Δ = -192-4·(-1)·36
Δ = 505
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{-(-19)-\sqrt{505}}{2*-1}=\frac{19-\sqrt{505}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{505}}{2*-1}=\frac{19+\sqrt{505}}{-2}
$