(2x+5)(3x-12)=0

Solution for (2x+5)(3x-12)=0 equation:

(2x+5)(3x-12)=0

We multiply parentheses ..

(+6x^2-24x+15x-60)=0

We get rid of parentheses

6x^2-24x+15x-60=0

We add all the numbers together, and all the variables

6x^2-9x-60=0

a = 6; b = -9; c = -60;
Δ = b2-4ac
Δ = -92-4·6·(-60)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-39}{2*6}=\frac{-30}{12}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+39}{2*6}=\frac{48}{12}
=4
$