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

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

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

We multiply parentheses ..

(+2x^2+24x-5x-60)=0

We get rid of parentheses

2x^2+24x-5x-60=0

We add all the numbers together, and all the variables

2x^2+19x-60=0

a = 2; b = 19; c = -60;
Δ = b2-4ac
Δ = 192-4·2·(-60)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-29}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+29}{2*2}=\frac{10}{4}
=2+1/2
$