343x^2-42x-1=0

Solution for 343x^2-42x-1=0 equation:

343x^2-42x-1=0

a = 343; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·343·(-1)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-56}{2*343}=\frac{-14}{686}
=-1/49
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+56}{2*343}=\frac{98}{686}
=1/7
$