4k^2-192k+1132=0

Solution for 4k^2-192k+1132=0 equation:

4k^2-192k+1132=0

a = 4; b = -192; c = +1132;
Δ = b2-4ac
Δ = -1922-4·4·1132
Δ = 18752
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18752}=\sqrt{64*293}=\sqrt{64}*\sqrt{293}=8\sqrt{293}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-8\sqrt{293}}{2*4}=\frac{192-8\sqrt{293}}{8}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+8\sqrt{293}}{2*4}=\frac{192+8\sqrt{293}}{8}
$