(x-4)(x+21)=0

Solution for (x-4)(x+21)=0 equation:

(x-4)(x+21)=0

We multiply parentheses ..

(+x^2+21x-4x-84)=0

We get rid of parentheses

x^2+21x-4x-84=0

We add all the numbers together, and all the variables

x^2+17x-84=0

a = 1; b = 17; c = -84;
Δ = b2-4ac
Δ = 172-4·1·(-84)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-25}{2*1}=\frac{-42}{2}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+25}{2*1}=\frac{8}{2}
=4
$