0=12x^2-192x+527

Solution for 0=12x^2-192x+527 equation:

0=12x^2-192x+527

We move all terms to the left:

0-(12x^2-192x+527)=0

We add all the numbers together, and all the variables

-(12x^2-192x+527)=0

We get rid of parentheses

-12x^2+192x-527=0

a = -12; b = 192; c = -527;
Δ = b2-4ac
Δ = 1922-4·(-12)·(-527)
Δ = 11568
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11568}=\sqrt{16*723}=\sqrt{16}*\sqrt{723}=4\sqrt{723}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-4\sqrt{723}}{2*-12}=\frac{-192-4\sqrt{723}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+4\sqrt{723}}{2*-12}=\frac{-192+4\sqrt{723}}{-24}
$