x(x+100)-196=0

Solution for x(x+100)-196=0 equation:

x(x+100)-196=0

We multiply parentheses

x^2+100x-196=0

a = 1; b = 100; c = -196;
Δ = b2-4ac
Δ = 1002-4·1·(-196)
Δ = 10784
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:

$\sqrt{\Delta}=\sqrt{10784}=\sqrt{16*674}=\sqrt{16}*\sqrt{674}=4\sqrt{674}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{674}}{2*1}=\frac{-100-4\sqrt{674}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{674}}{2*1}=\frac{-100+4\sqrt{674}}{2}
$