100a^2-4a-1=0

Solution for 100a^2-4a-1=0 equation:

100a^2-4a-1=0

a = 100; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·100·(-1)
Δ = 416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{26}}{2*100}=\frac{4-4\sqrt{26}}{200}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{26}}{2*100}=\frac{4+4\sqrt{26}}{200}
$