(x-2012)(3x-8)=0

Solution for (x-2012)(3x-8)=0 equation:

(x-2012)(3x-8)=0

We multiply parentheses ..

(+3x^2-8x-6036x+16096)=0

We get rid of parentheses

3x^2-8x-6036x+16096=0

We add all the numbers together, and all the variables

3x^2-6044x+16096=0

a = 3; b = -6044; c = +16096;
Δ = b2-4ac
Δ = -60442-4·3·16096
Δ = 36336784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36336784}=6028$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6044)-6028}{2*3}=\frac{16}{6}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6044)+6028}{2*3}=\frac{12072}{6}
=2012
$