X2+2x-263=0

Solution for X2+2x-263=0 equation:

X2+2X-263=0

We add all the numbers together, and all the variables

X^2+2X-263=0

a = 1; b = 2; c = -263;
Δ = b2-4ac
Δ = 22-4·1·(-263)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{66}}{2*1}=\frac{-2-4\sqrt{66}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{66}}{2*1}=\frac{-2+4\sqrt{66}}{2}
$