(x+5)(x-4)=-19

Solution for (x+5)(x-4)=-19 equation:

(x+5)(x-4)=-19

We move all terms to the left:

(x+5)(x-4)-(-19)=0

We add all the numbers together, and all the variables

(x+5)(x-4)+19=0

We multiply parentheses ..

(+x^2-4x+5x-20)+19=0

We get rid of parentheses

x^2-4x+5x-20+19=0

We add all the numbers together, and all the variables

x^2+x-1=0

a = 1; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·1·(-1)
Δ = 5
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{5}}{2*1}=\frac{-1-\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5}}{2*1}=\frac{-1+\sqrt{5}}{2}
$