12x^2-192x+572=0

Solution for 12x^2-192x+572=0 equation:

12x^2-192x+572=0

a = 12; b = -192; c = +572;
Δ = b2-4ac
Δ = -1922-4·12·572
Δ = 9408
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:

$\sqrt{\Delta}=\sqrt{9408}=\sqrt{3136*3}=\sqrt{3136}*\sqrt{3}=56\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-56\sqrt{3}}{2*12}=\frac{192-56\sqrt{3}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+56\sqrt{3}}{2*12}=\frac{192+56\sqrt{3}}{24}
$