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 = 9996
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:

$\sqrt{\Delta}=\sqrt{9996}=\sqrt{196*51}=\sqrt{196}*\sqrt{51}=14\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-14\sqrt{51}}{2*1}=\frac{-100-14\sqrt{51}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+14\sqrt{51}}{2*1}=\frac{-100+14\sqrt{51}}{2}
$