(X-3)(x+16)=0

Solution for (X-3)(x+16)=0 equation:

(X-3)(X+16)=0

We multiply parentheses ..

(+X^2+16X-3X-48)=0

We get rid of parentheses

X^2+16X-3X-48=0

We add all the numbers together, and all the variables

X^2+13X-48=0

a = 1; b = 13; c = -48;
Δ = b2-4ac
Δ = 132-4·1·(-48)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-19}{2*1}=\frac{-32}{2}
=-16
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+19}{2*1}=\frac{6}{2}
=3
$