(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+39x-60=0

a = -6; b = 39; c = -60;
Δ = b2-4ac
Δ = 392-4·(-6)·(-60)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-9}{2*-6}=\frac{-48}{-12}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+9}{2*-6}=\frac{-30}{-12}
=2+1/2
$