x2+14x-196=0

Solution for x2+14x-196=0 equation:

x2+14x-196=0

We add all the numbers together, and all the variables

x^2+14x-196=0

a = 1; b = 14; c = -196;
Δ = b2-4ac
Δ = 142-4·1·(-196)
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14\sqrt{5}}{2*1}=\frac{-14-14\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14\sqrt{5}}{2*1}=\frac{-14+14\sqrt{5}}{2}
$