49a^2+2a-1=0

Solution for 49a^2+2a-1=0 equation:

49a^2+2a-1=0

a = 49; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·49·(-1)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10\sqrt{2}}{2*49}=\frac{-2-10\sqrt{2}}{98}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10\sqrt{2}}{2*49}=\frac{-2+10\sqrt{2}}{98}
$