(2x-1)(6-3x)=0

Solution for (2x-1)(6-3x)=0 equation:

(2x-1)(6-3x)=0

We add all the numbers together, and all the variables

(2x-1)(-3x+6)=0

We multiply parentheses ..

(-6x^2+12x+3x-6)=0

We get rid of parentheses

-6x^2+12x+3x-6=0

We add all the numbers together, and all the variables

-6x^2+15x-6=0

a = -6; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·(-6)·(-6)
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{-(15)-9}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*-6}=\frac{-6}{-12}
=1/2
$