X2-196x+400=0

Solution for X2-196x+400=0 equation:

X2-196X+400=0

We add all the numbers together, and all the variables

X^2-196X+400=0

a = 1; b = -196; c = +400;
Δ = b2-4ac
Δ = -1962-4·1·400
Δ = 36816
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:

$\sqrt{\Delta}=\sqrt{36816}=\sqrt{16*2301}=\sqrt{16}*\sqrt{2301}=4\sqrt{2301}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-4\sqrt{2301}}{2*1}=\frac{196-4\sqrt{2301}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+4\sqrt{2301}}{2*1}=\frac{196+4\sqrt{2301}}{2}
$