X^2+100x-1=0

Solution for X^2+100x-1=0 equation:

X^2+100X-1=0

a = 1; b = 100; c = -1;
Δ = b2-4ac
Δ = 1002-4·1·(-1)
Δ = 10004
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:

$\sqrt{\Delta}=\sqrt{10004}=\sqrt{4*2501}=\sqrt{4}*\sqrt{2501}=2\sqrt{2501}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2501}}{2*1}=\frac{-100-2\sqrt{2501}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2501}}{2*1}=\frac{-100+2\sqrt{2501}}{2}
$