x^2+14x-227=0

Solution for x^2+14x-227=0 equation:

x^2+14x-227=0

a = 1; b = 14; c = -227;
Δ = b2-4ac
Δ = 142-4·1·(-227)
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-4\sqrt{69}}{2*1}=\frac{-14-4\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+4\sqrt{69}}{2*1}=\frac{-14+4\sqrt{69}}{2}
$