(x-47)(x+11)=0

Solution for (x-47)(x+11)=0 equation:

(x-47)(x+11)=0

We multiply parentheses ..

(+x^2+11x-47x-517)=0

We get rid of parentheses

x^2+11x-47x-517=0

We add all the numbers together, and all the variables

x^2-36x-517=0

a = 1; b = -36; c = -517;
Δ = b2-4ac
Δ = -362-4·1·(-517)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-58}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+58}{2*1}=\frac{94}{2}
=47
$