(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^2-29x+60=0

a = 2; b = -29; c = +60;
Δ = b2-4ac
Δ = -292-4·2·60
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-19}{2*2}=\frac{10}{4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+19}{2*2}=\frac{48}{4}
=12
$