(x+47)(x-5)=0

Solution for (x+47)(x-5)=0 equation:

(x+47)(x-5)=0

We multiply parentheses ..

(+x^2-5x+47x-235)=0

We get rid of parentheses

x^2-5x+47x-235=0

We add all the numbers together, and all the variables

x^2+42x-235=0

a = 1; b = 42; c = -235;
Δ = b2-4ac
Δ = 422-4·1·(-235)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-52}{2*1}=\frac{-94}{2}
=-47
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+52}{2*1}=\frac{10}{2}
=5
$