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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

-2x^2+5x+24x-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{-48}{-4}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+19}{2*-2}=\frac{-10}{-4}
=2+1/2
$