(2x-5)(4x+12)=0

Solution for (2x-5)(4x+12)=0 equation:

(2x-5)(4x+12)=0

We multiply parentheses ..

(+8x^2+24x-20x-60)=0

We get rid of parentheses

8x^2+24x-20x-60=0

We add all the numbers together, and all the variables

8x^2+4x-60=0

a = 8; b = 4; c = -60;
Δ = b2-4ac
Δ = 42-4·8·(-60)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-44}{2*8}=\frac{-48}{16}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+44}{2*8}=\frac{40}{16}
=2+1/2
$