(x-5)(x+10)=-54

Solution for (x-5)(x+10)=-54 equation:

(x-5)(x+10)=-54

We move all terms to the left:

(x-5)(x+10)-(-54)=0

We add all the numbers together, and all the variables

(x-5)(x+10)+54=0

We multiply parentheses ..

(+x^2+10x-5x-50)+54=0

We get rid of parentheses

x^2+10x-5x-50+54=0

We add all the numbers together, and all the variables

x^2+5x+4=0

a = 1; b = 5; c = +4;
Δ = b2-4ac
Δ = 52-4·1·4
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3}{2*1}=\frac{-2}{2}
=-1
$