(5x-1)(3x+12)=0

Solution for (5x-1)(3x+12)=0 equation:

(5x-1)(3x+12)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

15x^2+57x-12=0

a = 15; b = 57; c = -12;
Δ = b2-4ac
Δ = 572-4·15·(-12)
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-63}{2*15}=\frac{-120}{30}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+63}{2*15}=\frac{6}{30}
=1/5
$