1272*x^2-424*x+32=0

Solution for 1272*x^2-424*x+32=0 equation:

1272x^2-424x+32=0

a = 1272; b = -424; c = +32;
Δ = b2-4ac
Δ = -4242-4·1272·32
Δ = 16960
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:

$\sqrt{\Delta}=\sqrt{16960}=\sqrt{64*265}=\sqrt{64}*\sqrt{265}=8\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-424)-8\sqrt{265}}{2*1272}=\frac{424-8\sqrt{265}}{2544}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-424)+8\sqrt{265}}{2*1272}=\frac{424+8\sqrt{265}}{2544}
$