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