x^2-52x+196=0

Solution for x^2-52x+196=0 equation:

x^2-52x+196=0

a = 1; b = -52; c = +196;
Δ = b2-4ac
Δ = -522-4·1·196
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-8\sqrt{30}}{2*1}=\frac{52-8\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+8\sqrt{30}}{2*1}=\frac{52+8\sqrt{30}}{2}
$