0=-3x^2+20x-12

Solution for 0=-3x^2+20x-12 equation:

0=-3x^2+20x-12

We move all terms to the left:

0-(-3x^2+20x-12)=0

We add all the numbers together, and all the variables

-(-3x^2+20x-12)=0

We get rid of parentheses

3x^2-20x+12=0

a = 3; b = -20; c = +12;
Δ = b2-4ac
Δ = -202-4·3·12
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16}{2*3}=\frac{4}{6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16}{2*3}=\frac{36}{6}
=6
$