x^2-20x=196

Solution for x^2-20x=196 equation:

x^2-20x=196

We move all terms to the left:

x^2-20x-(196)=0

a = 1; b = -20; c = -196;
Δ = b2-4ac
Δ = -202-4·1·(-196)
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{74}}{2*1}=\frac{20-4\sqrt{74}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{74}}{2*1}=\frac{20+4\sqrt{74}}{2}
$