49x^2-56x+1=0

Solution for 49x^2-56x+1=0 equation:

49x^2-56x+1=0

a = 49; b = -56; c = +1;
Δ = b2-4ac
Δ = -562-4·49·1
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-14\sqrt{15}}{2*49}=\frac{56-14\sqrt{15}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+14\sqrt{15}}{2*49}=\frac{56+14\sqrt{15}}{98}
$