(x-5)(3x+12)=0

Solution for (x-5)(3x+12)=0 equation:

(x-5)(3x+12)=0

We multiply parentheses ..

(+3x^2+12x-15x-60)=0

We get rid of parentheses

3x^2+12x-15x-60=0

We add all the numbers together, and all the variables

3x^2-3x-60=0

a = 3; b = -3; c = -60;
Δ = b2-4ac
Δ = -32-4·3·(-60)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-27}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+27}{2*3}=\frac{30}{6}
=5
$