50x^2+100x-1=0

Solution for 50x^2+100x-1=0 equation:

50x^2+100x-1=0

a = 50; b = 100; c = -1;
Δ = b2-4ac
Δ = 1002-4·50·(-1)
Δ = 10200
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:

$\sqrt{\Delta}=\sqrt{10200}=\sqrt{100*102}=\sqrt{100}*\sqrt{102}=10\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{102}}{2*50}=\frac{-100-10\sqrt{102}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{102}}{2*50}=\frac{-100+10\sqrt{102}}{100}
$