x^2+8x-1414=0

Solution for x^2+8x-1414=0 equation:

x^2+8x-1414=0

a = 1; b = 8; c = -1414;
Δ = b2-4ac
Δ = 82-4·1·(-1414)
Δ = 5720
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:

$\sqrt{\Delta}=\sqrt{5720}=\sqrt{4*1430}=\sqrt{4}*\sqrt{1430}=2\sqrt{1430}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{1430}}{2*1}=\frac{-8-2\sqrt{1430}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{1430}}{2*1}=\frac{-8+2\sqrt{1430}}{2}
$