0=-12x2+20x-3

Solution for 0=-12x2+20x-3 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

12x^2-20x+3=0

a = 12; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·12·3
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*12}=\frac{4}{24}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16}{2*12}=\frac{36}{24}
=1+1/2
$